$S{I}_2$-quasicontinuous spaces

In this paper, as a common generalization of $S{I}_2$-continuous spaces and $s_2$-quasicontinuous posets, we introduce the concepts of $S{I}_2$-quasicontinuous spaces and $\mathcal{G}\mathcal{D}$-convergence of nets for arbitrary topological spaces by the cuts. Some characterizations of $S{I}_2$-quasicontinuity of spaces are given. The main results are: (1) a space is $S{I}_2$-quasicontinuous if and only if its weakly irreducible topology is hypercontinuous under inclusion order; (2) A $T_0$ space $X$ is $S{I}_2$-quasicontinuous if and only if the $\mathcal{G}\mathcal{D}$-convergence in $X$ is topological.