Quasihomeomorphisms and Some Topological Properties

Khedidja Dourari, Alaa M. Abd El-latif, Sami Lazaar, Abdelwaheb Mhemdi and Tareq M. Al-shami ()
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Khedidja Dourari: Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri University, Constantine 1, Constantine 25000, Algeria
Alaa M. Abd El-latif: Mathematics Department, Faculty of Arts and Science, Northern Border University, Rafha 91911, Saudi Arabia
Sami Lazaar: Department of Mathematics, Faculty of Sciences, University of Taibah, Madina 41311, Saudi Arabia
Abdelwaheb Mhemdi: Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdulaziz University, Riyadh 16273, Saudi Arabia
Tareq M. Al-shami: Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen

Mathematics, 2023, vol. 11, issue 23, 1-8

Abstract: In this paper, we study the properties of topological spaces preserved by quasihomeomorphisms. Particularly, we show that quasihomeomorphisms preserve Whyburn, weakly Whyburn, submaximal and door properties. Moreover, we offer necessary conditions on continuous map q : X → Y where Y is Whyburn (resp., weakly Whyburn ) in order to render X Whyburn (resp., weakly Whyburn). Also, we prove that if q : X → Y is a one-to-one continuous map and Y is submaximal (resp., door), then X is submaximal (resp., door). Finally, we close this paper by studying the relation between quasihomeomorphisms and k -primal spaces.

Keywords: quasihomeomorphism; Alexandroff space; Whyburn space; submaximal space; primal space; factorisation systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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