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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