Separability and minimal weak base topologies

Abstract

In this note, we present filter characterizations of minimal weakly first countable, minimal F \mathcal {F} , minimal F r {\mathcal {F}_r} , weakly first countable-closed, F \mathcal {F} -closed, and F r {\mathcal {F}_r} -closed spaces. Our main result is a generalization of G. M. Reed’s theorem that every Moore-closed space is separable.