Topological indistinguishability
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 Nx is the set of all neighborhoods that contain x, and Ny is the set of all neighborhoods that contain y, then x and y are "topologically indistinguishable" if and only if Nx = Ny.(See Hausdorff's axiomatic neighborhood systems.) Intuitively, two points are topologically indistinguishable if the topology of X is unable to discern between the points.
Wikipage disambiguates
CofinitenessFinite topological spaceGeneral topologyHausdorff spaceIndistinguishabilityKolmogorov spaceLimit of a sequenceOpen setOverlapping interval topologyPartition topologyRegular spaceSeparated setsSeparation axiomSierpiński spaceSpecialization (pre)orderT1 spaceTopological distinguishabilityTopologically distinguishableTopologically indistinguishableTrivial topology
Link from a Wikipage to another Wikipage
primaryTopic
Topological indistinguishability
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 Nx is the set of all neighborhoods that contain x, and Ny is the set of all neighborhoods that contain y, then x and y are "topologically indistinguishable" if and only if Nx = Ny.(See Hausdorff's axiomatic neighborhood systems.) Intuitively, two points are topologically indistinguishable if the topology of X is unable to discern between the points.
has abstract
En topologia, dos punts d'un e ...... en qualsevol espai topològic.
@ca
En topología, dos puntos de un ...... cualquier espacio topológico.
@es
In de topologie, een deelgebie ...... e maken tussen de twee punten.
@nl
In topology, two points of a t ...... s of x will be denoted by [x].
@en
在拓扑学中，拓扑空间X內的两点若有完全相同的鄰域，便稱這兩個 ...... 撲不可區分的，便標記成x ≡ y；x的等價類則標記為[x]。
@zh
Wikipage page ID
14,671,319
page length (characters) of wiki page
Wikipage revision ID
866,794,982
Link from a Wikipage to another Wikipage
wikiPageUsesTemplate
comment
En topologia, dos punts d'un e ...... al qual no perteneix l'altre.
@ca
En topología, dos puntos de un ...... cualquier espacio topológico.
@es
In de topologie, een deelgebie ...... e topologisch onderscheidbaar.
@nl
In topology, two points of a t ...... to discern between the points.
@en
在拓扑学中，拓扑空间X內的两点若有完全相同的鄰域，便稱這兩個 ...... 撲不可區分的，便標記成x ≡ y；x的等價類則標記為[x]。
@zh
label
Indistingibilitat topològica
@ca
Indistinguibilidad topológica
@es
Topological indistinguishability
@en
Topologische onderscheidbaarheid
@nl
拓扑不可区分性
@zh