Properties of theta-H-compact sets in hereditary m-spaces

Abstract

Let (X,m, H) be a hereditary m-space. A subset A of X is said to be θ-H-compact relative to X if for every cover U of A by m(θ)-open sets of X, there exists a finite subset U₀ of U such that A \ ∪ U₀ ∈ H. We obtain several properties of these sets. Also, we define and investigate two kinds of strong forms of “θ-H-compact relative to X”.