Properties of $m\mathcal H$-compact sets in hereditary $m$-spaces

Ahmad Al-Omari^a, Takashi Noiri<sup>b

a</sup> Department of Mathematics, Faculty of Sciences, Al al-Bayt University, Mafraq 25113, Jordan
^b Yatsushiro-shi, Kumamoto-ken, Japan

Abstract: 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.

UDC: 517

Received: 01.10.2024
Received in revised form: 06.11.2024
Accepted: 10.01.2025

Language: English