论文标题
$ si_2 $ - quasicontinule空间
$SI_2$-quasicontinuous spaces
论文作者
论文摘要
In this paper, as a common generalization of $SI_{2}$-continuous spaces and $s_{2}$-quasicontinuous posets, we introduce the concepts of $SI_{2}$-quasicontinuous spaces and $\mathcal{GD}$-convergence of nets for arbitrary topological spaces by the cuts.给出了$ si_ {2} $的一些特征 - 空间的准倾斜度。主要结果是：（1）空间为$ si_ {2} $ - 在包含顺序下其弱不可约束的拓扑时，仅当其弱不可约束的拓扑是超连续的； （2）a $ t_ {0} $ space $ x $ is $ si_ {2} $ - 仅当$ x $ in $ x $中的$ \ mathcal {gd} $ - convergence in $ x $是拓扑。
In this paper, as a common generalization of $SI_{2}$-continuous spaces and $s_{2}$-quasicontinuous posets, we introduce the concepts of $SI_{2}$-quasicontinuous spaces and $\mathcal{GD}$-convergence of nets for arbitrary topological spaces by the cuts. Some characterizations of $SI_{2}$-quasicontinuity of spaces are given. The main results are: (1) a space is $SI_{2}$-quasicontinuous if and only if its weakly irreducible topology is hypercontinuous under inclusion order; (2) A $T_{0}$ space $X$ is $SI_{2}$-quasicontinuous if and only if the $\mathcal{GD}$-convergence in $X$ is topological.
