| 代数结构上的模糊拟伪$b$-度量 |
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| 引用本文： | 韦健偲,盛业青,谢利红,李丕余.代数结构上的模糊拟伪$b$-度量[J].数学研究及应用,2024,44(3):397-407. |
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| 作者姓名： | 韦健偲 盛业青 谢利红 李丕余 |
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| 作者单位： | 五邑大学数学与计算科学学院, 广东 江门 529020;徐州工程学院数学与统计学院, 江苏 徐州 221018 |
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| 基金项目： | 广东省自然科学基金(Grant No.2021A1515010381), 广东省普通高校特色创新项目(Grant No.2022KTSCX145). |
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| 摘 要： | 研究代数结构上的模糊(拟)伪$b$-度量. 主要结论有: (1)设$G$是一个抽象群, $\tau$是$G$上一个左不变模糊拟伪$b$-度量(伪$b$-度量)诱导的拓扑,如果$(G,\tau)$是右拓扑群,那么$(G,\tau)$是一个仿拓扑群(拓扑群); (2)设$S$是一个半群,如果$\tau$是$S$上一个不变模糊拟伪$b$-度量诱导的拓扑,那么$(S,\tau)$是一个拓扑半群.
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| 关 键 词： | 左拓扑群 右拓扑群 半拓扑群 仿拓扑群 拓扑群 拓扑半群 模糊拟伪$b$-度量 不变模糊(拟)伪$b$-度量 |
| 收稿时间： | 2023/5/16 0:00:00 |
| 修稿时间： | 2023/11/16 0:00:00 |
Fuzzy Quasi-Pseudo-$b$-Metrics on Algebraic Structures |
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| Jiancai WEI,Yeqing SHENG,Lihong XIE,Piyu LI.Fuzzy Quasi-Pseudo-$b$-Metrics on Algebraic Structures[J].Journal of Mathematical Research with Applications,2024,44(3):397-407. |
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| Authors: | Jiancai WEI Yeqing SHENG Lihong XIE Piyu LI |
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| Institution: | School of Mathematics and Computational Science, Wuyi University, Guangdong 529020, P. R. China; 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 |
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| Keywords: | 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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