More on almost countably compact spaces

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 {Un : n ∈ N} of X, there is a finite subfamily {Uni}mi=1, where m ∈ N such that X = ∪mi=1 Cl(Uni). In particular, we investigate this new class of spaces and some other properties in the view of regular cover notion and semiregularization topology. © 2020 Forum-Editrice Universitaria Udinese SRL. All rights reserved.