Nearly Countably Compact Spaces

Abstract

New class of spaces is introduced in this paper as a generalization of countably compact spaces called nearly countably compact spaces. Some characterizations and results about this new class of spaces are also presented. We give a definition of more generalized kind of spaces and we call it nearly regular countably compact spaces. Also, we study the effect of some mappings on the nearly countably compact spaces.

On Countably $α$-Compact Topological Spaces

“…Typically, α-closure of a subset of a topological space X is the intersection of each α-closed set containing it and denoted by Cl α (A) where A ⊆ X whereas α-interior of a subset is the union of each α-open set contained in it and denoted by Int α (B) where B ⊆ X [5]. The g-closure of a subset D of X denoted by Cl * (D) is the intersection of the g-closed sets containing D [6]. The family of α-open subsets of X is denoted by αO(X) and the family of α-closed subsets of X is denoted by αC(X).…”

Nearly µ-Lindelöfness Via Hereditary Class

“…Among them, the most important and the best-known are in Császár space [1] which are studied in this paper, infra-topological spaces [2], per-topologies [3], minimal spaces [4], weak structures [5] and, finally, generalized weak structures [6] (which are just arbitrary collections of sets). Some other generalizations have been done on covering properties in different ways as [8][9][10][11][12][13].…”

Weakly Covering Spaces in Coc-open Sets

“…It is clearly that regularly open is an open set. For further studied in regular open spaces in covering spaces and separation axioms, see [1][2][3][4][5].…”