ON A FINER TOPOLOGICAL SPACE THAN ?? AND SOME MAPS

In 1943, Fomin [7] introduced the notion of theta-continuity. In 1966, the notions of theta-open subsets, theta-closed subsets and theta-closure were introduced by Velieko [18] for the purpose of studying the important class of H-closed spaces in terms of arbitrary filterbases. He also showed that the collection of theta-open sets in a topological space (X,tau) forms a topology on X denoted by tau(theta) (see also [12]). Dickman and Porter [4], [5], Joseph [11] continued the work of Velieko. Noiri and Jafari [15], Caldas et al. [1] and [2], Steiner [16] and Cao et al [3] have also obtained several new and interesting results related to these sets. In this paper, we will offer a finer topology on X than tau(theta) by utilizing the new notions of omega(theta)-open and omega(theta)-closed sets. We will also discuss some of the fundamental properties of such sets and some related maps.