H-closed space

An **H-closed space** is a concept from topology, typically used in the study of general topological spaces. A topological space \( X \) is said to be **H-closed** if every open cover of \( X \) has a finite subcover, but only if every totally bounded subset of \( X \) is relatively compact. In simpler terms, H-closed spaces are spaces where every continuous map from a compact space into \( X \) is closed.