  The aim of this paper is to define and study $\mathcal{B}$-open sets and
related properties. 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. Using $\mathcal{B}$-open sets, we introduce a
number of concepts such as $\mathcal{B}$-dense, $\mathcal{B}$-Frechet,
contra-$\mathcal{B}$-closed graph and contra-$\mathcal{B}$-continuity. Also, we
define a bi-operator topological space $(X, \tau, T_1, T_2)$ which involves two
operators $T_1$ and $T_2$, which are used to define $\mathcal{B}$-open sets.
