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On Topological and Metric Properties of ⊕-sb-Metric Spaces

Author

Listed:
  • Alexander Šostak

    (Institute of Mathematics and CS, University of Latvia, LV-1459 Riga, Latvia
    Department of Mathematics, University of Latvia, LV-1004 Riga, Latvia)

  • Tarkan Öner

    (Department of Mathematics, Muğla Sıtkı Koçman University, Muğla 48000, Turkey)

  • İlyas Can Duman

    (Department of Mathematics, Graduate School of Natural and Applied Sciences, Muğla Sıtkı Koçman University, Muğla 48000, Turkey)

Abstract

In this paper, we study ⊕-sb-metric spaces, which were introduced to generalize the concept of strong b-metric spaces. In particular, we study the properties of the topology induced via an ⊕-sb metric (separation properties, countability axioms, etc.), prove the continuity of the ⊕-sb-metric, establish the metrizability of the ⊕-sb-metric spaces of countable weight, discuss the convergence structure of an ⊕-sb-metric space and prove the Baire category type theorem for such spaces. Most of the results obtained here are new already for strong b-metric spaces, i.e., in the case where an arithmetic sum “+” is taken in the role of ⊕.

Suggested Citation

  • Alexander Šostak & Tarkan Öner & İlyas Can Duman, 2023. "On Topological and Metric Properties of ⊕-sb-Metric Spaces," Mathematics, MDPI, vol. 11(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4090-:d:1248846
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    References listed on IDEAS

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    1. María A. Navascués & Sangita Jha & Arya K. B. Chand & Ram N. Mohapatra, 2023. "Iterative Schemes Involving Several Mutual Contractions," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
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