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.