Concerning Cut Point Spaces of Order Three
A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Her...
Ausführliche Beschreibung
Autor*in: |
D. Daniel [verfasserIn] William S. Mahavier [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2007 |
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Übergeordnetes Werk: |
In: International Journal of Mathematics and Mathematical Sciences - Hindawi Limited, 2008, (2007) |
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Übergeordnetes Werk: |
year:2007 |
Links: |
Link aufrufen |
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DOI / URN: |
10.1155/2007/10679 |
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Katalog-ID: |
DOAJ025275585 |
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10.1155/2007/10679 doi (DE-627)DOAJ025275585 (DE-599)DOAJ154c0b96ef86438bb55148c870793b2f DE-627 ger DE-627 rakwb eng QA1-939 D. Daniel verfasserin aut Concerning Cut Point Spaces of Order Three 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. Mathematics William S. Mahavier verfasserin aut In International Journal of Mathematics and Mathematical Sciences Hindawi Limited, 2008 (2007) (DE-627)302721657 (DE-600)1492203-4 16870425 nnns year:2007 https://doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/article/154c0b96ef86438bb55148c870793b2f kostenfrei http://dx.doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/toc/0161-1712 Journal toc kostenfrei https://doaj.org/toc/1687-0425 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2007 |
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10.1155/2007/10679 doi (DE-627)DOAJ025275585 (DE-599)DOAJ154c0b96ef86438bb55148c870793b2f DE-627 ger DE-627 rakwb eng QA1-939 D. Daniel verfasserin aut Concerning Cut Point Spaces of Order Three 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. Mathematics William S. Mahavier verfasserin aut In International Journal of Mathematics and Mathematical Sciences Hindawi Limited, 2008 (2007) (DE-627)302721657 (DE-600)1492203-4 16870425 nnns year:2007 https://doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/article/154c0b96ef86438bb55148c870793b2f kostenfrei http://dx.doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/toc/0161-1712 Journal toc kostenfrei https://doaj.org/toc/1687-0425 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2007 |
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10.1155/2007/10679 doi (DE-627)DOAJ025275585 (DE-599)DOAJ154c0b96ef86438bb55148c870793b2f DE-627 ger DE-627 rakwb eng QA1-939 D. Daniel verfasserin aut Concerning Cut Point Spaces of Order Three 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. Mathematics William S. Mahavier verfasserin aut In International Journal of Mathematics and Mathematical Sciences Hindawi Limited, 2008 (2007) (DE-627)302721657 (DE-600)1492203-4 16870425 nnns year:2007 https://doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/article/154c0b96ef86438bb55148c870793b2f kostenfrei http://dx.doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/toc/0161-1712 Journal toc kostenfrei https://doaj.org/toc/1687-0425 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2007 |
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10.1155/2007/10679 doi (DE-627)DOAJ025275585 (DE-599)DOAJ154c0b96ef86438bb55148c870793b2f DE-627 ger DE-627 rakwb eng QA1-939 D. Daniel verfasserin aut Concerning Cut Point Spaces of Order Three 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. Mathematics William S. Mahavier verfasserin aut In International Journal of Mathematics and Mathematical Sciences Hindawi Limited, 2008 (2007) (DE-627)302721657 (DE-600)1492203-4 16870425 nnns year:2007 https://doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/article/154c0b96ef86438bb55148c870793b2f kostenfrei http://dx.doi.org/10.1155/2007/10679 kostenfrei https://doaj.org/toc/0161-1712 Journal toc kostenfrei https://doaj.org/toc/1687-0425 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ 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_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2007 |
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Concerning Cut Point Spaces of Order Three |
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A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. |
abstractGer |
A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. |
abstract_unstemmed |
A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space. |
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title_short |
Concerning Cut Point Spaces of Order Three |
url |
https://doi.org/10.1155/2007/10679 https://doaj.org/article/154c0b96ef86438bb55148c870793b2f http://dx.doi.org/10.1155/2007/10679 https://doaj.org/toc/0161-1712 https://doaj.org/toc/1687-0425 |
remote_bool |
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author2 |
William S. Mahavier |
author2Str |
William S. Mahavier |
ppnlink |
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callnumber-subject |
QA - Mathematics |
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doi_str |
10.1155/2007/10679 |
callnumber-a |
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up_date |
2024-07-03T14:02:01.646Z |
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