Authors: E. Ekici, Saeid Jafari, R. M. Latif
In 1943, Fomin [7] introduced the notion of θ-continuity. In 1966, the notions of θ-open subsets, θ-closed subsets and θ-closure were introduced by Veliˇcko [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 θ-open sets in a topological space (X, τ ) forms a topology on X denoted by τ θ (see also [12]). Dickman and Porter [4], [5], Joseph [11] continued the work of Veliˇcko. 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 ωθ-open and ωθ-closed sets. We will also discuss some of the fundamental properties of such sets and some related maps.
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