Convergence in %$s_{2}%$-quasicontinuous posets

Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of po...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ruan, Xiao-jun [verfasserIn] Xu, Xiao-quan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	-Continuous poset -Quasicontinuous poset Weak Scott topology -Convergence

Übergeordnetes Werk:	Enthalten in: SpringerPlus - London : Biomed Central, 2012, 5(2016), 1 vom: 29. Feb.
Übergeordnetes Werk:	volume:5 ; year:2016 ; number:1 ; day:29 ; month:02

Links:	Volltext

DOI / URN:	10.1186/s40064-016-1873-6

Katalog-ID:	SPR03277723X

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520			\|a Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological.
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allfields	10.1186/s40064-016-1873-6 doi (DE-627)SPR03277723X (SPR)s40064-016-1873-6-e DE-627 ger DE-627 rakwb eng 600 ASE Ruan, Xiao-jun verfasserin aut Convergence in %$s_{2}%$-quasicontinuous posets 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological. -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 Xu, Xiao-quan verfasserin aut Enthalten in SpringerPlus London : Biomed Central, 2012 5(2016), 1 vom: 29. Feb. (DE-627)718615298 (DE-600)2661116-8 2193-1801 nnns volume:5 year:2016 number:1 day:29 month:02 https://dx.doi.org/10.1186/s40064-016-1873-6 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1 29 02
spelling	10.1186/s40064-016-1873-6 doi (DE-627)SPR03277723X (SPR)s40064-016-1873-6-e DE-627 ger DE-627 rakwb eng 600 ASE Ruan, Xiao-jun verfasserin aut Convergence in %$s_{2}%$-quasicontinuous posets 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological. -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 Xu, Xiao-quan verfasserin aut Enthalten in SpringerPlus London : Biomed Central, 2012 5(2016), 1 vom: 29. Feb. (DE-627)718615298 (DE-600)2661116-8 2193-1801 nnns volume:5 year:2016 number:1 day:29 month:02 https://dx.doi.org/10.1186/s40064-016-1873-6 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1 29 02
allfields_unstemmed	10.1186/s40064-016-1873-6 doi (DE-627)SPR03277723X (SPR)s40064-016-1873-6-e DE-627 ger DE-627 rakwb eng 600 ASE Ruan, Xiao-jun verfasserin aut Convergence in %$s_{2}%$-quasicontinuous posets 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological. -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 Xu, Xiao-quan verfasserin aut Enthalten in SpringerPlus London : Biomed Central, 2012 5(2016), 1 vom: 29. Feb. (DE-627)718615298 (DE-600)2661116-8 2193-1801 nnns volume:5 year:2016 number:1 day:29 month:02 https://dx.doi.org/10.1186/s40064-016-1873-6 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1 29 02
allfieldsGer	10.1186/s40064-016-1873-6 doi (DE-627)SPR03277723X (SPR)s40064-016-1873-6-e DE-627 ger DE-627 rakwb eng 600 ASE Ruan, Xiao-jun verfasserin aut Convergence in %$s_{2}%$-quasicontinuous posets 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological. -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 Xu, Xiao-quan verfasserin aut Enthalten in SpringerPlus London : Biomed Central, 2012 5(2016), 1 vom: 29. Feb. (DE-627)718615298 (DE-600)2661116-8 2193-1801 nnns volume:5 year:2016 number:1 day:29 month:02 https://dx.doi.org/10.1186/s40064-016-1873-6 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1 29 02
allfieldsSound	10.1186/s40064-016-1873-6 doi (DE-627)SPR03277723X (SPR)s40064-016-1873-6-e DE-627 ger DE-627 rakwb eng 600 ASE Ruan, Xiao-jun verfasserin aut Convergence in %$s_{2}%$-quasicontinuous posets 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological. -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213 Xu, Xiao-quan verfasserin aut Enthalten in SpringerPlus London : Biomed Central, 2012 5(2016), 1 vom: 29. Feb. (DE-627)718615298 (DE-600)2661116-8 2193-1801 nnns volume:5 year:2016 number:1 day:29 month:02 https://dx.doi.org/10.1186/s40064-016-1873-6 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_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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2016 1 29 02
language	English
source	Enthalten in SpringerPlus 5(2016), 1 vom: 29. Feb. volume:5 year:2016 number:1 day:29 month:02
sourceStr	Enthalten in SpringerPlus 5(2016), 1 vom: 29. Feb. volume:5 year:2016 number:1 day:29 month:02
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	-Continuous poset -Quasicontinuous poset Weak Scott topology -Convergence
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isfreeaccess_bool	true
container_title	SpringerPlus
authorswithroles_txt_mv	Ruan, Xiao-jun @@aut@@ Xu, Xiao-quan @@aut@@
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author	Ruan, Xiao-jun
spellingShingle	Ruan, Xiao-jun ddc 600 misc -Continuous poset misc -Quasicontinuous poset misc Weak Scott topology misc -Convergence Convergence in %$s_{2}%$-quasicontinuous posets
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topic_title	600 ASE Convergence in %$s_{2}%$-quasicontinuous posets -Continuous poset (dpeaa)DE-He213 -Quasicontinuous poset (dpeaa)DE-He213 Weak Scott topology (dpeaa)DE-He213 -Convergence (dpeaa)DE-He213
topic	ddc 600 misc -Continuous poset misc -Quasicontinuous poset misc Weak Scott topology misc -Convergence
topic_unstemmed	ddc 600 misc -Continuous poset misc -Quasicontinuous poset misc Weak Scott topology misc -Convergence
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title	Convergence in %$s_{2}%$-quasicontinuous posets
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title_full	Convergence in %$s_{2}%$-quasicontinuous posets
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title_sort	convergence in %$s_{2}%$-quasicontinuous posets
title_auth	Convergence in %$s_{2}%$-quasicontinuous posets
abstract	Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological.
abstractGer	Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological.
abstract_unstemmed	Abstract In this paper, we present one way to generalize %${\mathcal {S}}%$-convergence and %${\mathcal {GS}}%$-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of %$s_2%$-continuity and %$s_2%$-quasicontinuity of posets are given. The main results are: (1) a poset P is %$s_2%$-continuous if and only if the %${\mathcal {S}}%$-convergence in P is topological; (2) P is %$s_2%$-quasicontinuous if and only if the %${\mathcal {GS}}%$-convergence in P is topological.
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title_short	Convergence in %$s_{2}%$-quasicontinuous posets
url	https://dx.doi.org/10.1186/s40064-016-1873-6
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up_date	2024-07-03T14:43:59.407Z
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score	7.400032

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Convergence in %$s_{2}%$-quasicontinuous posets

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Zugang & Verfügbarkeit

Vorhandene Bände

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