# Hausdorff Space

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## Hausdorff space

[′hau̇s·dȯrf ‚spās]
(mathematics)
A topological space where each pair of distinct points can be enclosed in disjoint open neighborhoods. Also known as T2 space.

## Hausdorff Space

in mathematics, an important type of to pological space. A Hausdorff space is a topological space wherein any two points have nonintersecting neighborhoods. Such spaces were first defined in 1914 by F. Hausdorff, who carried out a detailed study of them.

References in periodicals archive ?
[S.sub.1] is said to be g[ALEPH] Hausdorff space or [T.sub.2] space if for any two [ALEPH]--sets A and B with A [intersection] B = [0.sub.~],there exist g[ALEPH] open sets U and V, such that A [??] U,B [??] V and U [intersection] V = [0.sub.~].
In , a result (Theorem 1 on page 27) is given describing the density of a subset of C(X,K)[cross product]Y in C(X,Y) for a Tikhonov space X and topological linear Hausdorff space Y over K (again in the compact-open topology).
P.Nanzetta and D Plank  extended some characterization to an arbitrary completely regular Hausdorff space X and derived some corollaries.
Let S = ([s.sub.n]) be a sequence of self-maps on a Hausdorff space X.
Let Xbea compact Hausdorff space, let G be a finite group acting freely on [S.sup.n] and let H be a cyclic subgroup of G of order prime p.
Let X be a convex space and Y a Hausdorff space. More early in 1997 , we introduced a 'better' admissible class B of multimaps as follows:
It follows that the spectrum [bar.S] of A is a compact Hausdorff space. Furthermore, since points of S determine complex homomorphisms of A, there is a continuous map [alpha] : S [right arrow] [bar.S], with dense image, such that f [??] fo[alpha] : C([bar.S]) [right arrow] A is an isometric isomorphism of C([bar.S]) onto A, when [alpha] is injective.
Aldrich (2014) offers an example in topology with the statement: "A compact Hausdorff space is normal".
A New Form of Fuzzy Hausdorff Space and Related Topics via Fuzzy Idealization, IOSR Journal of Mathematics (IOSR-JM), Volume 3, Issue 5 (Sep.-Oct.
In this paper, I present the definition of soft bitopological Hausdorff space and construct some basic properties.
If X is an [A]-[theta]-paracompact Hausdorff space, then it is [A]-[theta]-regular.

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