Maximal Soft Compact and Maximal Soft Connected Topologies

In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the pr...

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Bibliographic Details
Published in:Applied Computational Intelligence and Soft Computing Vol. 2022; pp. 1 - 7
Main Authors: Al Ghour, Samer, Ameen, Zanyar A.
Format: Journal Article
Language:English
Published: New York Hindawi 08.02.2022
John Wiley & Sons, Inc
Wiley
Subjects:
Fuzzy sets
Game theory
Set theory
Topology
ISSN:1687-9724, 1687-9732
Online Access:Get full text
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Summary:In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal, and some are minimal with respect to specific soft topological properties. We study the properties of soft compact and soft connected topologies that are maximal. Particularly, we prove that a maximal soft compact topology has identical families of soft compact and soft closed sets. We further show that a maximal soft compact topology is soft T1, while a maximal soft connected topology is soft T0. Lastly, we establish that each soft connected relative topology to a maximal soft connected topology is maximal.
Bibliography:ObjectType-Article-1
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ISSN:1687-9724
1687-9732
DOI:10.1155/2022/9860015