On the \(\eta\)-expansion topology for the co-semi-regularization and mildly Hausdorff spaces (Q1288896)

The paper deals with the study of the relations between some special classes of topological spaces. The authors introduce the class of the mildly Hausdorff spaces which contains the weakly Hausdorff spaces, the \(R_1\)-spaces, the strongly \(s\)-regular spaces and which is contained in the class of \(R_0\)-spaces. Among others they prove that every weakly mildly Hausdorff, locally re-paracompact space is extremally disconnected and that a space is weakly Hausdorff if and only if it is an almost weakly Hausdorff space and a mildly Hausdorff space. Finally the authors state that a topological product of mildly Hausdorff spaces is a mildly Hausdorff space.