On generalized topologies arising from mappings

Abstract

Given a mapping $f:Xto X$ we naturally associate to it a monotonic <br />map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, <br />thus inducing a generalized topology on $X$. In this paper we <br />investigate some properties of generalized topologies which are <br />defined by such a procedure.