Classical vs. non-Archimedean analysis: an approach via algebraic genericity

Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiabilit...
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Autor*in:	Fernández-Sánchez, J. [verfasserIn] Maghsoudi, S. Rodríguez-Vidanes, D. L. Seoane-Sepúlveda, J. B.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	-adic numbers -adic continuous function -adic differentiable function -adic sequences lineability algebrability spaceability Cesàro summable non-absolutely convergent series Liouville’s theorem Lipschitz condition Hahn–Banach theorem

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Heidelberg [u.a.] : Springer, 2001, 116(2022), 2 vom: 29. Jan.
Übergeordnetes Werk:	volume:116 ; year:2022 ; number:2 ; day:29 ; month:01

Links:	Volltext

DOI / URN:	10.1007/s13398-022-01209-5

Katalog-ID:	SPR046100482

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520			\|a Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem.
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912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
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912			\|a GBV_ILN_2118
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912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
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912			\|a GBV_ILN_4307
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allfields	10.1007/s13398-022-01209-5 doi (DE-627)SPR046100482 (SPR)s13398-022-01209-5-e DE-627 ger DE-627 rakwb eng Fernández-Sánchez, J. verfasserin aut Classical vs. non-Archimedean analysis: an approach via algebraic genericity 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213 Maghsoudi, S. aut Rodríguez-Vidanes, D. L. (orcid)0000-0002-1016-096X aut Seoane-Sepúlveda, J. B. aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 116(2022), 2 vom: 29. Jan. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:116 year:2022 number:2 day:29 month:01 https://dx.doi.org/10.1007/s13398-022-01209-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 116 2022 2 29 01
spelling	10.1007/s13398-022-01209-5 doi (DE-627)SPR046100482 (SPR)s13398-022-01209-5-e DE-627 ger DE-627 rakwb eng Fernández-Sánchez, J. verfasserin aut Classical vs. non-Archimedean analysis: an approach via algebraic genericity 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213 Maghsoudi, S. aut Rodríguez-Vidanes, D. L. (orcid)0000-0002-1016-096X aut Seoane-Sepúlveda, J. B. aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 116(2022), 2 vom: 29. Jan. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:116 year:2022 number:2 day:29 month:01 https://dx.doi.org/10.1007/s13398-022-01209-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 116 2022 2 29 01
allfields_unstemmed	10.1007/s13398-022-01209-5 doi (DE-627)SPR046100482 (SPR)s13398-022-01209-5-e DE-627 ger DE-627 rakwb eng Fernández-Sánchez, J. verfasserin aut Classical vs. non-Archimedean analysis: an approach via algebraic genericity 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213 Maghsoudi, S. aut Rodríguez-Vidanes, D. L. (orcid)0000-0002-1016-096X aut Seoane-Sepúlveda, J. B. aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 116(2022), 2 vom: 29. Jan. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:116 year:2022 number:2 day:29 month:01 https://dx.doi.org/10.1007/s13398-022-01209-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 116 2022 2 29 01
allfieldsGer	10.1007/s13398-022-01209-5 doi (DE-627)SPR046100482 (SPR)s13398-022-01209-5-e DE-627 ger DE-627 rakwb eng Fernández-Sánchez, J. verfasserin aut Classical vs. non-Archimedean analysis: an approach via algebraic genericity 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213 Maghsoudi, S. aut Rodríguez-Vidanes, D. L. (orcid)0000-0002-1016-096X aut Seoane-Sepúlveda, J. B. aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 116(2022), 2 vom: 29. Jan. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:116 year:2022 number:2 day:29 month:01 https://dx.doi.org/10.1007/s13398-022-01209-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 116 2022 2 29 01
allfieldsSound	10.1007/s13398-022-01209-5 doi (DE-627)SPR046100482 (SPR)s13398-022-01209-5-e DE-627 ger DE-627 rakwb eng Fernández-Sánchez, J. verfasserin aut Classical vs. non-Archimedean analysis: an approach via algebraic genericity 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213 Maghsoudi, S. aut Rodríguez-Vidanes, D. L. (orcid)0000-0002-1016-096X aut Seoane-Sepúlveda, J. B. aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 116(2022), 2 vom: 29. Jan. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:116 year:2022 number:2 day:29 month:01 https://dx.doi.org/10.1007/s13398-022-01209-5 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 116 2022 2 29 01
language	English
source	Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 116(2022), 2 vom: 29. Jan. volume:116 year:2022 number:2 day:29 month:01
sourceStr	Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 116(2022), 2 vom: 29. Jan. volume:116 year:2022 number:2 day:29 month:01
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	-adic numbers -adic continuous function -adic differentiable function -adic sequences lineability algebrability spaceability Cesàro summable non-absolutely convergent series Liouville’s theorem Lipschitz condition Hahn–Banach theorem
isfreeaccess_bool	true
container_title	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales
authorswithroles_txt_mv	Fernández-Sánchez, J. @@aut@@ Maghsoudi, S. @@aut@@ Rodríguez-Vidanes, D. L. @@aut@@ Seoane-Sepúlveda, J. B. @@aut@@
publishDateDaySort_date	2022-01-29T00:00:00Z
hierarchy_top_id	495744433
id	SPR046100482
language_de	englisch
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Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. 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author	Fernández-Sánchez, J.
spellingShingle	Fernández-Sánchez, J. misc -adic numbers misc -adic continuous function misc -adic differentiable function misc -adic sequences misc lineability misc algebrability misc spaceability misc Cesàro summable misc non-absolutely convergent series misc Liouville’s theorem misc Lipschitz condition misc Hahn–Banach theorem Classical vs. non-Archimedean analysis: an approach via algebraic genericity
authorStr	Fernández-Sánchez, J.
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topic_title	Classical vs. non-Archimedean analysis: an approach via algebraic genericity -adic numbers (dpeaa)DE-He213 -adic continuous function (dpeaa)DE-He213 -adic differentiable function (dpeaa)DE-He213 -adic sequences (dpeaa)DE-He213 lineability (dpeaa)DE-He213 algebrability (dpeaa)DE-He213 spaceability (dpeaa)DE-He213 Cesàro summable (dpeaa)DE-He213 non-absolutely convergent series (dpeaa)DE-He213 Liouville’s theorem (dpeaa)DE-He213 Lipschitz condition (dpeaa)DE-He213 Hahn–Banach theorem (dpeaa)DE-He213
topic	misc -adic numbers misc -adic continuous function misc -adic differentiable function misc -adic sequences misc lineability misc algebrability misc spaceability misc Cesàro summable misc non-absolutely convergent series misc Liouville’s theorem misc Lipschitz condition misc Hahn–Banach theorem
topic_unstemmed	misc -adic numbers misc -adic continuous function misc -adic differentiable function misc -adic sequences misc lineability misc algebrability misc spaceability misc Cesàro summable misc non-absolutely convergent series misc Liouville’s theorem misc Lipschitz condition misc Hahn–Banach theorem
topic_browse	misc -adic numbers misc -adic continuous function misc -adic differentiable function misc -adic sequences misc lineability misc algebrability misc spaceability misc Cesàro summable misc non-absolutely convergent series misc Liouville’s theorem misc Lipschitz condition misc Hahn–Banach theorem
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title	Classical vs. non-Archimedean analysis: an approach via algebraic genericity
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title_full	Classical vs. non-Archimedean analysis: an approach via algebraic genericity
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author-letter	Fernández-Sánchez, J.
doi_str_mv	10.1007/s13398-022-01209-5
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title_sort	classical vs. non-archimedean analysis: an approach via algebraic genericity
title_auth	Classical vs. non-Archimedean analysis: an approach via algebraic genericity
abstract	Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. © The Author(s) 2022
abstractGer	Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. © The Author(s) 2022
abstract_unstemmed	Abstract In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem. © The Author(s) 2022
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container_issue	2
title_short	Classical vs. non-Archimedean analysis: an approach via algebraic genericity
url	https://dx.doi.org/10.1007/s13398-022-01209-5
remote_bool	true
author2	Maghsoudi, S. Rodríguez-Vidanes, D. L. Seoane-Sepúlveda, J. B.
author2Str	Maghsoudi, S. Rodríguez-Vidanes, D. L. Seoane-Sepúlveda, J. B.
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doi_str	10.1007/s13398-022-01209-5
up_date	2024-07-03T20:21:24.760Z
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Classical vs. non-Archimedean analysis: an approach via algebraic genericity

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