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Quasihomeomorphisms and Some Topological Properties

Author

Listed:
  • 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)

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.

Suggested Citation

  • Khedidja Dourari & Alaa M. Abd El-latif & Sami Lazaar & Abdelwaheb Mhemdi & Tareq M. Al-shami, 2023. "Quasihomeomorphisms and Some Topological Properties," Mathematics, MDPI, vol. 11(23), pages 1-8, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4748-:d:1286747
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