• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.775-784
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• 2024

Let (X, m, 𝓗) be a hereditary m-space and γ : m → P(X) be an operation on m. A subset A of X is said to be γ𝓗-compact relative to X [3] if for every cover {U_𝛼 : 𝛼 ∈ 2206;} of A by m-open sets of X, there exists a finite subset ∆₀ of ∆ such that A ⧵ ∪{γ(U_𝛼) : 𝛼 ∈ ∆₀} ∈ 𝓗. In this paper, we define and investigate two kinds of strong forms of γ𝓗-compact relative to X.