| Fuzzy Quasi-Pseudo-$b$-Metrics on Algebraic Structures |
| Received:May 16, 2023 Revised:November 16, 2023 |
| Key Words:
left topological group right topological group semitopological group paratopological group topological group topological semigroup fuzzy quasi-pseudo-$b$-metric invariant fuzzy (quasi-)pseudo-$b$-metric
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| Fund Project:Supported by the Natural Science Foundation of Guangdong Province (Grant No.2021A1515010381) and the Innovation Project of Department of Education of Guangdong Province (Grant No.2022KTSCX145). |
| Author Name | Affiliation | | Jiancai WEI | School of Mathematics and Computational Science, Wuyi University, Guangdong 529020, P. R. China | | Yeqing SHENG | School of Mathematics and Computational Science, Wuyi University, Guangdong 529020, P. R. China | | Lihong XIE | School of Mathematics and Computational Science, Wuyi University, Guangdong 529020, P. R. China | | Piyu LI | School of Mathematics and Statistics, Xuzhou Institute of Technology, Jiangsu 221018, P. R. China |
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| Abstract: |
| In this paper, we mainly study fuzzy (quasi-)pseudo-$b$-metrics on algebraic structures. We mainly establish the following results: (1) If a group $G$ with a topology $\tau$, which is induced by a left invariant fuzzy quasi-pseudo-$b$-metric (resp., pseudo-$b$-metric) on the $G$, is a right topological group, then $G$ with the topology $\tau$ is a paratopological group (resp., a topological group) and (2) If a semigroup $S$ with a topology $\tau$ is induced by an invariant fuzzy quasi-pseudo-$b$-metric, then $S$ with the topology $\tau$ is a topological semigroup |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.03.010 |
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