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.

Mathematics Subject Classification (1991): 06D22, 54A20.

Key words: Frames; balanced filters; closed-generated filters;
ultrafilters.

Quaestiones Mathematicae 26(2003), 73-81.