In topology, a **metacompact space** is a type of topological space that has certain properties related to open covers. Specifically, a topological space \( X \) is called **metacompact** if every open cover of \( X \) has a point-finite open refinement. To break this down: 1. **Open Cover**: An open cover of a space \( X \) is a collection of open sets whose union contains \( X \).
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