Balanced and Closed-generated Filters In Frames

Abstract

We introduce the notions of balanced filters and closed-generated filters in frames and use them to give a new characterisation of normality for frames, and hence, due to normality being a conservative property, a new characterisation of normality for topological spaces. We also establish some results which are frame counterparts of known topological ones. In particular we show that in a regular frame free ultrafilters are regular iff free prime filters are ultrafilters.