Overview of Super-Compactness on Topological Spaces

Super compactness is a property of topological spaces that generalizes the concept of compactness. A topological space is super compact if every open cover has a finite sub-cover that is "super-refining," meaning that it can be further refined to an open cover with a smaller mesh. Super compactness was first introduced by E. Michael in his paper "A note on paracompact spaces" in 1951. In this paper, Michael introduced the concept of a super-refining open cover and proved that a space is super compact if and only if it is paracompact and has the property that every open cover has a super-refining open cover