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

Alexander Šostak (), Tarkan Öner and İlyas Can Duman
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Alexander Šostak: Institute of Mathematics and CS, University of Latvia, LV-1459 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

Mathematics, 2023, vol. 11, issue 19, 1-12

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 ⊕.

Keywords: extended t-conorm; ?-metric; strong b-metric; ?-sb-metric; topology induced via ?-sb-metric; Baire category theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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