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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.