Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SUPER AND STRONG γ𝓗-COMPACTNESS IN HEREDITARY m-SPACES

  • Ahmad Al-Omari (Department of Mathematics Faculty of Sciences Al al-Bayt University) ;
  • Takashi Noiri (Korean Mathematical Society)
  • Received : 2023.08.03
  • Accepted : 2024.04.16
  • Published : 2024.07.31
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Abstract

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 {U𝛼 : 𝛼 ∈ 2206;} of A by m-open sets of X, there exists a finite subset ∆0 of ∆ such that A ⧵ ∪{γ(U𝛼) : 𝛼 ∈ ∆0} ∈ 𝓗. In this paper, we define and investigate two kinds of strong forms of γ𝓗-compact relative to X.

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Acknowledgement

The authors are highly grateful to editors and referees for their valuable comments and suggestions for improving the paper.

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