Hausdorff Space

(redirected from Hausdorff topological space)

Hausdorff space

[′hau̇s·dȯrf ‚spās]
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 ?
In a neutrosophic Hausdorff topological space X, the following conditions are equivalent.
Indeed, Hewitt[10] has constructed a regular Hausdorff topological space S such that the only continuous real-valued functions on it are constant functions; in [9], Granirer defined a semi-topological semigroup structure on S by letting a.
If S is also a Hausdorff topological space and the binary operation is continuous for the product topology of S x S, then S is said to be a topological semigroup.
Let E be a Hausdorff topological space and U an open subset of E.
Recall that a completely regular Hausdorff topological space X is called Lindelof [SIGMA] (or K-countably determined) if there is an upper semi-continuous compact-valued map T from a non-empty subset [SIGMA] of the product space [N.
Let Top be the site defined by the category of (locally compact) Hausdorff topological spaces with the open covering Grothendieck topology (as in the "gros topos" of [5, [section]2]).