On Metric-Type Spaces Based on Extended T-Conorms
1
Department of Mathematics, Muğla Sıtkı Koçman University, Muğla 48000, Turkey
2
Institute of Mathematics and CS and Department of Mathematics, University of Latvia, LV-1586 Riga, Latvia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2020, 8(7), 1097; https://doi.org/10.3390/math8071097
Received: 10 June 2020 / Revised: 29 June 2020 / Accepted: 1 July 2020 / Published: 5 July 2020
(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures)
Kirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many properties that are similar to the properties of classic metric spaces. Having noticed the advantages of strong b-metric spaces Kirk and Shahzad complained about the absence of non-trivial examples of such spaces. It is the main aim of this paper to construct a series of strong b-metric spaces that fail to be metric. Realizing this programme, we found it reasonable to consider these metric-type spaces in the context when the ordinary sum operation is replaced by operation ⊕, where ⊕ is an extended t-conorm satisfying certain conditions.
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Keywords:
metric; b-metric; sb-metric; extended t-conorm; ⊕-metric; ⊕-b-metric; ⊕-sb-metric
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MDPI and ACS Style
Öner, T.; Šostak, A. On Metric-Type Spaces Based on Extended T-Conorms. Mathematics 2020, 8, 1097. https://doi.org/10.3390/math8071097
AMA Style
Öner T, Šostak A. On Metric-Type Spaces Based on Extended T-Conorms. Mathematics. 2020; 8(7):1097. https://doi.org/10.3390/math8071097
Chicago/Turabian StyleÖner, Tarkan; Šostak, Alexander. 2020. "On Metric-Type Spaces Based on Extended T-Conorms" Mathematics 8, no. 7: 1097. https://doi.org/10.3390/math8071097
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