Properties of HC -compactness in hereditary m-spaces

Abstract

Let (X, m, H) be a hereditary m-space. A subset A of X is said to be H_C -compact relative to X if for every cover U of A by m-open sets of X, there exists a finite subset U₀ of U such that A - ∪ {mCl(U_α) : α ∈ U₀} ∈ H. We obtain several properties of these sets. And also, we define and investigate nearly H_C -compact relative to X.