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 ?
The PN space under the strong topology is a Hausdorff space and satisfies the first countability axiom.
This will lead to a characterization of semi-strongly continuous functions f: X [right arrow] Y where Y is a first countable Hausdorff space.
It is shown that the space M(A) in the Gelfand topology is a compact Hausdorff space for every unital TQ-algebras with a nonempty set M(A), and a commutative complete metrizable unital algebra is a TQ-algebras if and only if all maximal topological ideals of A are closed.
m],m [greater than or equal to] 1, a topological combinatorial manifold Ml is a Hausdorff space such that for any point p [member of] [?
In the classical formulation of Size Theory, M is required to be a non-empty, compact and locally connected Hausdorff space, and [?
A local po-space is a Hausdorff space M with a covering U = {[U.
Recall that a Hausdorff space is said to be regular if for each closed subset F of X, p [member of] X\F, there exist disjoint open sets U, V such that p [member of] U, F [subset] V.
Let B be a compact topological Hausdorff space and X := C(B) the normed vector space of all real valued, continuous functions defined on B with norm || f || := [max.
That is, if [OMEGA] is a compact Hausdorff space and E is a real Banach space, suppose that [V.
Proof: - since A and B are disjoint closed sets in compact Hausdorff space W(X, G), then there are open sets [O.
15] A paracompact space (X, [tau]) is a Hausdorff space with the property that every open cover of X has an open locally finite refiniment.
Since A is commutative, there is a locally compact Hausdorff space X such that A [congruent to] [C.