Pseudo-Normality and Pseudo-Tychonoffness of Topological Groups

Mesfer H. Alqahtani, Hanan Al-Saadi (), Eman Alluqmani and Zanyar A. Ameen
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Mesfer H. Alqahtani: Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia
Hanan Al-Saadi: Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Eman Alluqmani: Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Zanyar A. Ameen: Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq

Mathematics, 2024, vol. 13, issue 1, 1-11

Abstract: It is common knowledge that any topological group that satisfies the lowest separation axiom, T 0 , is immediately Hausdorff and completely regular; however, this is not the case for normality. This motivates us to introduce the concept of pseudo-normal groups along with pseudo-Tychonoff topological groups as generalizations of the normality and Tychonoffness of topological groups, respectively. We show that every pseudo-normal (resp. pseudo-Tychonoff) topological group is normal (resp. Tychonoff). Generally, the reverse implication of the latter does not hold. Then, we discuss their main properties in detail. To clarify these properties, we provide some examples. Finally, we establish some other results.

Keywords: topological group; pseudo-normal topological group; pseudo-Tychonoff topological group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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