On the Hausdorff open continuous images of Hausdorff paracompact $p$-spaces

On soft Hausdorff spaces

The aim of this paper is to study some properties of soft Hausdorff space introduced by Shabir and Naz. Firstly, we give a representation of soft sets and soft topological spaces. Secondly, we introduce some new concepts in soft topological space such as convergence of sequences, homeomorphism and investigate the relations between these concepts and Hausdorff axiom in soft topological space. 20...

Continuous Functions on Products of Compact Hausdorff Spaces

In the original version of the present paper submitted in 1995, we stated: "As far as we know it may be possible to prove that, if H and K are two compact Hausdorff spaces and (C(H), pointwise) and (C(K), pointwise) are both a-fragmented, then (C(HxK), pointwise) is also a-fragmented. If this is so, then the condition that for each finite subset O of F the space C(U {Kv: (pe}, pointwise) is ...

Extensions of Hausdorff Spaces

On the Characterization of Hausdorff Spaces

In this paper A, B, X, Y denote sets. Let X be an empty set. Note that ⋃ X is empty. Next we state several propositions: (1) (δX) ◦A ⊆ [:A, A :]. (2) (δX) ([:A, A :]) ⊆ A. (3) For every subset A of X holds (δX) ([:A, A :]) = A. (4) dom〈π2(X×Y ), π1(X×Y )〉 = [:X, Y :] and rng〈π2(X×Y ), π1(X×Y )〉 = [:Y, X :]. (5) 〈π2(X × Y ), π1(X × Y )〉 ◦[:A, B :] ⊆ [:B, A :]. (6) For every subset A of X and for...

On the cardinality of functionally Hausdorff spaces

In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If X is a functionally Hausdorff space then |X| ≤ 2fs(X)ψτ (X); (ii) Let X be a functionally Hausdorff space with fs(X) ≤ κ. Then there is a subset S of X such that |S| ≤ 2 and X = S {clτθ(A) : A ∈ [S] }.