Super and Strong γ H-Lindel¨ofness in Hereditary m-Spaces

Abstract

Let (X, m, H) be a hereditary m-space and γ : m → P(X) be a γ-operation on m. A subset A of X is said to be γH-Lindel¨of relative to X [1] if for every cover {Uα : α ∈ ∆} of A by m-open sets of X, there exists a countable subset ∆0 of ∆ such that A \ ∪{γ(Uα) : α ∈ ∆0} ∈ H. In this paper, we define and investigate two kinds of strong forms of “γ H-Lindel¨of relative to X”.

Keywords

• hereditary m-space
• γH-Lindel¨ofness
• strong γH-Lindel¨ofness
• super γH-Lindel¨ofness.

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