More on almost countably compact spaces

Abstract

We study a recent general space of countably compact space called almost countably compact.  A topological space X is almost countably compact space if for every countable open cover {U_n : n ∈ \(\mathbb{N}\)} of X, there is a finite subfamily {U\(_{n_i}\)}\(_{i=1}^{m}\) where m ∈ \(\mathbb{N}\) such that X = \(\bigcup\)\(_{i=1}^{m}\) Cl(U\(_{n_i}\)).  In particular, we investigate this new class of spaces and some other properties in the view of regular cover notion and semiregularization topology.