Geodesic
Properties of $m\mathcal H$-compact sets in hereditary $m$-spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 2, pp. 262-272

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Let $(X, m, \mathcal{H})$ be a hereditary $m$-space. A subset $A$ of $X$ is said to be $\mathcal{H}$-compact relative to $X$ if for every cover $\mathcal U$ of $A$ by $m$-open sets of $X$, there exists a finite subset $\mathcal{U}_0$ of $\mathcal{U}$ such that $A \setminus \cup\ \mathcal{U}_0 \in$ $\mathcal{H}$. We obtain several properties of these sets. And also, we define and investigate two kinds of strong forms of $\mathcal{H}$-compact relative to $X$.
Keywords: hereditary $m$-space, $\mathcal H$-compactness, strong $\mathcal H$-compactness, super $\mathcal H$-compactness. 
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     title = {Properties of $m\mathcal H$-compact sets in hereditary $m$-spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Ahmad Al-Omari; Takashi Noiri. Properties of $m\mathcal H$-compact sets in hereditary $m$-spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 2, pp. 262-272. http://geodesic.mathdoc.fr/item/JSFU_2025_18_2_a11/