论文标题
一步封闭，理想收敛和单调确定空间
One-step Closure, Ideal Convergence and Monotone Determined Space
论文作者
论文摘要
单调确定的空间是DCPO的自然拓扑扩展。它的主要目的是为领域理论构建扩展框架。在本文中，我们研究了单调确定空间的一步封闭和理想收敛。然后，我们还介绍了C空间和局部超紧张空间的等效表征。主要结果是：1。每个C空间都具有一步的闭合，并且每个局部超紧张的空间的一步闭合； 2.一个单调确定的空间在且仅当它是D-Meet连续且一步较弱的一步闭合时具有一步的闭合。 3. IS-Convergence（分别IGS-Convergence）是拓扑Iff X是C空间（分别是局部超相相空间）； 4.如果X是D-Meet连续空间，那么以下三个条件相当：（i）X为C空间； （ii）与劳森拓扑相对于X的X iff（XJ）I-CONCONGES的净（XJ）ISL相位； （iii）与劳森拓扑相对于X的X IGSL（XJ）IGSL连接到X。
Monotone determined spaces are natural topological extensions of dcpo. Its main purpose is to build an extended framework for domain theory. In this paper, we study the one-step closure and ideal convergence on monotone determined space. Then we also introduce the equivalent characterizations of c-spaces and locally hypercompact space. The main results are:1.Every c-space has one-step closure and every locally hypercompact space has weak one-step closure;2.A monotone determined space has one-step closure if and only if it is d-meet continuous and has weak one-step closure. 3.IS-convergence(resp. IGS-convergence) is topological iff X is a c-space (resp. locally hypercompact space); 4.If X is a d-meet continuous space, then the following three conditions are equivalent to each other: (i) X is c-space; (ii) The net (xj ) ISL-converges to x iff (xj ) I-converges to x with respect to Lawson topology; (iii) The net (xj ) IGSL-converges to x iff (xj ) I-converges to x with respect to Lawson topology.
