On B-Open Sets

Layth Muhsin Habeeb Alabdulsada

Abstract

The aim of this paper is to introduce and study $\mathcal{B}$-open sets and related properties. Also, we define a bi-operator topological space $(X, \tau, T_1, T_2)$, involving the two operators $T_1$ and $T_2$, which are used to define $\mathcal{B}$-open sets. A $\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is, in turn, a generalization of a pre-open set and a semi-open set. We introduce a number of concepts based on $\mathcal{B}$-open sets.

Keywords

operator topological space, bi-operator topological space, $\mathcal{B}$-open sets, $T^*$-open sets, contra-$\mathcal{B}$-continuous, Urysohn space, weakly Hausdorff space

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