Fuzzy quasi-psedo-$b$-metrics on algebraic structures

英文关键词: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

中文摘要:

      

英文摘要:

      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 $\tau$, which is induced by an invariant fuzzy quasi-pseudo-$b$-metric, then $S$ with the topology $\tau$ is a topological semigroup.