topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
and related branches of mathematics, a Hausdorff space ( , ), separated space or T2 space is a
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called po ...
where, for any two distinct points, there exist
neighbourhoods
A neighbourhood (British English, Irish English, Australian English and Canadian English) or neighborhood (American English; see spelling differences) is a geographically localised community within a larger city, town, suburb or rural ar ...
of each which are
disjoint
Disjoint may refer to:
*Disjoint sets, sets with no common elements
*Mutual exclusivity, the impossibility of a pair of propositions both being true
See also
*Disjoint union
*Disjoint-set data structure
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{{DEFAULTSORT:Hausdorff Space
Separation axiomsProperties of topological spaces