A comparative study of compactness on topological spaces and pretopological spaces

Abstract

Pretopological spaces are generalized topological spaces that can serve as valuable tools for structuring intricate systems. Nevertheless, there remains a considerable amount of work within the realm of pretopology theory that needs to be done. The concepts of closure or neighborhood can be harnessed to establish the foundations of pretopology. This paper delves into the new defnitions of compactness within pretopological space, oering both an exploration of these ideas and a comparative analysis alongside topological space.