拓扑系统中的闭包元和闭包集及其相关性质

doi:10.6040/j.issn.1671-9352.0.2021.340

摘要/Abstract

摘要： 由于拓扑系统中闭元的缺失,对拓扑系统中与闭集相关内容的理论及性质研究受到一定程度的制约。首先利用余frame和点集两部分建立对偶拓扑系统——由闭元确定的拓扑系统,对其基本性质进行初步讨论;其次利用闭元给出点集部分的闭包元概念,并对闭包元性质进行讨论;第三,利用闭包元给出拓扑系统中凝聚点和导集的定义,对导集和闭包集的性质进行讨论。最后总结讨论闭包元和闭包集的关系。

关键词: 余frame, 拓扑系统, 闭包元, 凝聚点, 导集, 闭包集

Abstract: Because of the lack of closed elements in topological systems, the research on the theory and properties of closed sets in topological systems is restricted to a certain extent. In this paper, the dual topological system, the topological system determined by closed elements, is established by using the coframe and the point set, and its basic properties are discussed. Secondly, the concept of closure element of point set part is given by using closed element, and the properties of closure element are discussed. Thirdly, the definition of condensation point and derived set in topological system is given by using closure element, and the properties of derived set and closure set are discussed. Finally, the relationship between closure element and closure set is discussed.

Key words: coframe, topological system, closure element, condensation point, derived set, closure set

中图分类号:

O189.1

高雅,吴洪博. 拓扑系统中的闭包元和闭包集及其相关性质[J]. 《山东大学学报(理学版)》, 2022, 57(4): 30-36.

GAO Ya, WU Hong-bo. Closure elements and closure sets in topological systems and their related properties[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 30-36.

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