Pairwise semi paracompact spaces

Strongly base-paracompact spaces

A space X is said to be strongly base-paracompact if there is a basis B for X with |B| = w(X) such that every open cover of X has a star-finite open refinement by members of B. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions F with cardinality equal to the weight such that every open cover has a l...

Separation in Countably Paracompact Spaces

We study the question "Are discrete families of points separated in countably paracompact spaces?" in the class of first countable spaces and the class of separable spaces. Two of the main directions of research in general topology in the last thirty years have been the work of Jones, Bing, Tall, Fleissner, Nyikos and others motivated by the normal Moore space problem (when are discrete familie...

A Note on Paracompact Spaces

Let us quickly recall the definitions of the terms which are used in the statement of Theorem 1, and which will be used throughout this paper. Let X be a topological space. A collection <R of subsets of X is called open (resp. closed) if every element of "R. is open (resp. closed) in X. A covering of X is a collection of subsets of X whose union is X; observe that in this paper a covering need ...

Soft Connected Spaces and Soft Paracompact Spaces

On a Class of Countably Paracompact Spaces

In this note we shall characterize a topological property which is stronger than countable paracompactness but which is equivalent to it for normal spaces. A real valued function on a topological space X is locally bounded if each point has a neighborhood on which the function is bounded. Let C(X) denote the set of real valued continuous functions on X. A topological space is a cb-space if for ...