Quasicompactness and functionally Hausdorff spaces

Two cardinal inequalities for functionally Hausdorff spaces

In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τθ-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: ifX is a functionally Hausdorff space, then |X| ≤ 2χ(X)wcd(X).

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] }.

Modal compact Hausdorff spaces

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

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...

Extensions of Hausdorff Spaces