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  
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 NameAffiliation
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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