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# Article

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Keywords:
selections; l.s.c. set-valued maps; mesocompact; sequentially mesocompact; persevering compact set-valued maps
Summary:
A topological space $X$ is called mesocompact (sequentially mesocompact) if for every open cover ${\mathcal U}$ of $X$, there exists an open refinement ${\mathcal V}$ of ${\mathcal U}$ such that $\{V\in {\mathcal V}: V\cap K\neq \emptyset\}$ is finite for every compact set (converging sequence including its limit point) $K$ in $X$. In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory.
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