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Topological Indistinguishability
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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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130352677
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Sprache Englisch
- Größe H220mm x B150mm x T5mm
- Jahr 2010
- EAN 9786130352677
- Format Fachbuch
- ISBN 978-613-0-35267-7
- Titel Topological Indistinguishability
- Untertitel Topology, Topological Space, Neighbourhood (Mathematics), If and only If, Open Set, Kolmogorov Space, Closed Set, Equivalence Relation, Separation Axiom
- Gewicht 131g
- Herausgeber VDM Verlag Dr. Müller e.K.
- Anzahl Seiten 76
- Genre Mathematik
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