关于定向空间连续性的注记

doi:10.6040/j.issn.1671-9352.0.2024.279

摘要/Abstract

摘要： 定向空间的交连续性与连续性是研究拓扑空间的重要性质,本文给出一步闭包和弱一步闭包的概念,并研究它们与交连续空间的关系。利用定向扩展概率幂空间给出连续空间的等价刻画。如果定向空间有一步闭包,则其是交连续空间,定向空间是有弱一步闭包的交连续空间当且仅当其有一步闭包。如果定向空间的定向扩展概率幂空间连续,则定向空间是交连续的,定向空间是连续空间当且仅当其定向扩展概率幂空间是连续空间。

关键词: 定向空间, 交连续空间, 一步闭包, 连续空间, 定向扩展概率幂空间

Abstract: The continuity and meet continuity of directed spaces are important properties to study topological space. We give the concepts of one-step closure and weak one-step closure, and study their relationship with meet continuous spaces. An equivalent characterization of a continuous space is given using the directed probability powerspace. If the directed space has a one-step closure, then it is meet continuous space. The directed space is an meet continuous space with a weak one-step closure if and only if it has a one-step closure. If the directed probability powerspace of a directed space is continuous, then it is meet continuous. Furthermore, a directed space is continuous if and only if its directed probability powerspace is continuous.

Key words: directed space, meet continuous space, one step closure, continuous space, directed probability powerspace

中图分类号:

O153

王武. 关于定向空间连续性的注记[J]. 《山东大学学报(理学版)》, 2026, 61(4): 62-68.

WANG Wu. Notes on the continuity of directed spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(4): 62-68.

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