Prime $z$-filters on completely regular spaces
Prime $z$-filters on completely regular spaces
A prime z-filter on a space X is a proper prime dual ideal in the lattice Z(X) of zero-sets on X ; with no loss of generality, one may take the space to be completely regular [3, 3.9].Each prime z-filter is contained in a unique maximal z-filter (z-ultrafilter), and thus …