Topological properties of the class of generators of an indistinguishability operator

The present paper investigates the relations between topologies in the classical sense, fuzzy topologies in Lowenʹs sense and indistinguishability operators as well as constructing topologies and fuzzy topologies by means of indistinguishability operators. Furthermore, as a particular consequence of the results in this paper, a characterization theorem for pseudo-metrizable topological spaces in the classical sense is also surprisingly obtained.