Hemicompact space

A **hemicompact space** is a type of topological space that is defined based on the properties of its open cover. Specifically, a topological space \( X \) is called hemicompact if every open cover of \( X \) has a countable subcover that is also locally finite. To unpack this a little further: - **Open Cover**: A collection of open sets whose union contains the entire space \( X \).