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.
Highlights
Over the past years, an amount of generalizations of open sets has been considered
First we introduce and study the new notion of bi-operator topological spaces and its related properties
We investigate the relationships between these types of functions, besides we check the relationships with some special spaces such as Urysohn space or weakly Hausdorff space
Summary
An amount of generalizations of open sets has been considered. The first notion due to Levine [12] in 1963 was semi-open sets, while in 1965 Njastad [15] introduced some classes of nearly open sets, more precisely, they investigated the structure of α-open set and gave some applications. In 1996 [3], Andrijevic introduced and studied a new class of generalized open sets in a topological space, called b-open sets. All of these above concepts were defined using the closure operator Cl and the interior operator Int. This research area (which is fertile in information) still takes a significant part of the investigations because it has a clear effect on the development of the topological space through the experience of many theories and characteristics of different types of open sets, for instance see ([1], [17], [7], [8], [10], [9] and [21]). First we introduce and study the new notion of bi-operator topological spaces and its related properties. A number of important related properties are stated and proved
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