On Extremal Topology - Sola, Mabruk Ali (The Libyan Journal of Science, 2016)
Extremal topology was defined on an arbitrary set as a maximal non-discrete topology [2]. In this paper we will prove that every extremal topology on a set X has to be of the form , for some and some ultrafilter in . Where is the power set of . We also show that if is a free ultrafilter then is a space.