On the position of abstract density topologies in the lattice of all topologies

Abstract

This work refers to well known concept of abstract density topologies, semi-open sets and
some relation connected with these notions. Abstract density topologies were introduced by
O. Haupt and Ch. Pauc in 1952 ([4]). The properties of such topologies were extensively
examined by many mathematicians and we will make use of some of their results. The notion
of semi-open sets appeared in 1963 in the article of by N. Levine ([7]). He also dened the
relation of semi-correspondence between topologies. In the following paper we will show that
there is a very close and strict connection between those classical concepts.