ON CELLULAR-COUNTABLY-COMPACT SPACES

Abstract

A space X is said to be cellular-countably-compact [4, 11] if for each cellular family U of open sets in X, there is a countably compact subspace K of X such that U ∩ K ̸= ∅ for each U ∈ U. Cellular-countably-compact spaces generalize both countably compact spaces and cellular-compact spaces. In this paper, we study cellular-countably-compact spaces and investigate the relationship between cellular-countably-compact spaces and related spaces. By using Erd ̈os and Rad ́o’s theorem, we establish the cardinal inequalities for cellular-countably-compact spaces. Finally we study the topological behavior of cellular-countably-compact spaces on subspaces and products.