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

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

Taschenbuch - 9786130352677
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Beschreibung

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.

Details

Verlag Betascript Publishers
Ersterscheinung Februar 2010
Maße 220 mm x 150 mm x 5 mm
Gewicht 130 Gramm
Format Taschenbuch
ISBN-13 9786130352677
Auflage Nicht bekannt
Seiten 76

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