Fuzzy quasi-pseudometrics on algebraic structures

摘要

In this work we state a number of theorems about fuzzy (quasi-)pseudometrizable algebraic structures. Our most useful results are: (1) a fuzzy semitopological group whose topology is induced by a left-invariant fuzzy (quasi-)pseudometric, then it is a fuzzy (paratopological) topological group, (2) if the topology on a semigroup S is induced by an invariant fuzzy quasi- pseudometric, then S is a fuzzy topological semigroup, and (3) the same conclusion is valid for a left-invariant fuzzy quasi-pseudometric on a monoid G such that the left translations are open and the right translations are continuous at the identity e of G. By means of the standard fuzzy (quasi-) pseudometric M-d associated to a (quasi-) pseudometric d, our results apply in the case of semitopological groups, semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes. (C) 2017 Elsevier B.V. All rights reserved.