Publication: Study Of Irr-Topological Groups And Isocompactness For Locally Semi-Compact Spaces
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Date
2025-04
Authors
Wang, Zhongli
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Abstract
Over the years, generalized open sets have been a focal point of research for mathematicians. Many of the topological properties of locally semi-compact spaces remain unknown, and their connections with other topological spaces are still unclear. This work will focus on these problems and mainly consists of two parts. The first part focuses on the generalizations and applications of locally semi-compact spaces, while the second part primarily deals with the applications of isocompact spaces in locally compact topological groups. In the first part, we primarily accomplished three works. First, we obtain some new topological properties of locally semi-compact spaces, and introduce the new definition of semi-k spaces, which generalizes the concept of locally semi-compact. Second, the relations between separation axioms and locally semi-compact spaces, between semi-countably compact spaces and semi-k spaces, and between locally semi-compact spaces and s-paracompact spaces are established. Third, and most importantly, we obtain some applications of locally semi-compact spaces in s-topological groups and irr-topological groups. Additionally, we prove when locally
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General topology