SUPER AND STRONG γH-COMPACTNESS IN HEREDITARY m-SPACES
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Let $(X, m$, $\h)$ be a hereditary $m$-space and $\gamma : m \rightarrow P(X)$ be an operation on $m$. A subset $A$ of $X$ is said to be $\gamma\h$-compact relative to $X$ \cite{Al-No} if for every cover $\{ U_\alpha : \alpha \in \Delta \}$ of $A$ by $m$-open sets of $X$, there exists a finite subset $\Delta_0$ of $\Delta$ such that $A \setminus \cup\{ \gamma(U_\alpha) : \alpha \in \Delta_0 \} \in \h$. In this paper, we define and investigate two kinds of strong forms of $\gamma\h$-compact relative to $X$.
Abstract
Let $(X, m$, $\h)$ be a hereditary $m$-space and $\gamma : m \rightarrow P(X)$ be an operation on $m$. A subset $A$ of $X$ is said to be $\gamma\h$-compact relative to $X$ \cite{Al-No} if for every cover $\{ U_\alpha : \alpha \in \Delta \}$ of $A$ by $m$-open sets of $X$, there exists a finite subset $\Delta_0$ of $\Delta$ such that $A \setminus \cup\{ \gamma(U_\alpha) : \alpha \in \Delta_0 \} \in \h$. In this paper, we define and investigate two kinds of strong forms of $\gamma\h$-compact relative to $X$.
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