论文标题
$ \ MATHCAL {S} _X $ -CONVERGENCE和本地超紧张空间
$\mathcal{S}_X$-convergence and locally hypercompact spaces
论文作者
论文摘要
在本文中，我们为局部超紧张的空间提供了Scott Convergence定理的拓扑版本。我们在$ t_0 $拓扑空间$ x $上介绍了$ \ Mathcal {s}^*_ x $ -convergence的概念，并定义有限近似空间的概念。单调确定的空间是DCPO的自然拓扑扩展。主要结果是：（1）单调确定的空间$ x $是本地超稳定空间，如果$ \ mathcal {s}^*_ x $ -convergence是拓扑。 （2）对于$ t_0 $ space $ x $，$ \ mathcal {s}^*_ x $ -convergence是拓扑，如果$ x $是一个有限的近似空间。 （3）如果单调确定空间$ x $的Lawson拓扑紧凑，则$ x $是Scott拓扑结构的DCPO。
In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of $\mathcal{S}^*_X$-convergence on a $T_0$ topological space $X$, and define the notion of finitely approximated spaces. Monotone determined spaces are natural topological extensions of dcpos. The main results are: (1) A monotone determined space $X$ is a locally hypercompact space iff $\mathcal{S}^*_X$-convergence is topological. (2) For a $T_0$ space $X$, $\mathcal{S}^*_X$-convergence is topological iff $X$ is a finitely approximating space. (3) If the Lawson topology on a monotone determined space $X$ is compact, then $X$ is a dcpo endowed with the Scott topology.
