JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 30-36.doi: 10.6040/j.issn.1671-9352.0.2021.340

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Closure elements and closure sets in topological systems and their related properties

GAO Ya, WU Hong-bo*   

  1. College of Mathematics and Statistics, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2022-03-29

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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

CLC Number: 

  • O189.1
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