On Some Properties of e-Spaces

An open subset of a space is said to be e-open if its closure is also open and if a space has a base consisting of e-open sets, we call it an e-space. In this paper we first introduce e-spaces and compare them with relative spaces such as extremally disconnected and zerodimensional spaces. Subspaces of e-spaces and product of e-spaces are investigated and we define the concept of e-compactness and characterize e-compact spaces via e-convergence of nets and filters. We introduce e-separation axioms T e 1 − T e 4 and investigate the counterparts of results in the literature of topology concerning separation axioms. It is shown that a space is a T3 − e-space if and only if it is zero-dimensional and a space is a T e 4 -space if and only if it is a strongly zero-dimensional T4- space. In contrast to extremally disconnected spaces whose product is not necessarily an extremally disconnected space, we observe that any product of e-spaces is an e-space. Also we see that the e-closure of a set need not be e-closed, contrary to closure of a set which is closed.