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Topological Indistinguishability: Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom - Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
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Topological Indistinguishability: Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom - Taschenbuch

ISBN: 6130352670

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Topological Indistinguishability - Taschenbuch

ISBN: 6130352670

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Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom - Buch, gebundene Ausgabe, 76 S., Beilagen: Paperback, Erschienen: 2010 Betascript Publishers High Quality Content by WIKIPEDIA articles! In topology, two points of a topological space X are topologically indistinguishable if they have exactly the same neighborhoods. That is, if x and y are points in X, and A is the set of all neighborhoods which contain x, and B is the set of all neighborhoods which contain y, then x and y are 'topologically indistinguishable' if and only if A=B. Intuitively, two points are topologically indistinguishable if the topology of X is unable to discern between the points. Two points of X are topologically distinguishable if they are not topologically indistinguishable. This means there is an open set containing precisely one of the two points (equivalently, there is a closed set containing precisely one of the two points). This open set can then be used to distinguish between the two points. A T0 space is a topological space in which every pair of distinct points is topologically distinguishable. This is the weakest of the separation axioms.

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Topological Indistinguishability (Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom)
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Details zum Buch
Topological Indistinguishability: Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom

High Quality Content by WIKIPEDIA articles! In topology, two points of a topological space X are topologically indistinguishable if they have exactly the same neighborhoods. That is, if x and y are points in X, and A is the set of all neighborhoods which contain x, and B is the set of all neighborhoods which contain y, then x and y are 'topologically indistinguishable' if and only if A=B. Intuitively, two points are topologically indistinguishable if the topology of X is unable to discern between the points. Two points of X are topologically distinguishable if they are not topologically indistinguishable. This means there is an open set containing precisely one of the two points (equivalently, there is a closed set containing precisely one of the two points). This open set can then be used to distinguish between the two points. A T0 space is a topological space in which every pair of distinct points is topologically distinguishable. This is the weakest of the separation axioms.

Detailangaben zum Buch - Topological Indistinguishability: Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom


ISBN (ISBN-10): 6130352670
Gebundene Ausgabe
Taschenbuch

Buch in der Datenbank seit 31.07.2009 09:13:36
Buch zuletzt gefunden am 20.01.2012 21:34:21
ISBN/EAN: 6130352670

ISBN - alternative Schreibweisen:
613-0-35267-0


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