on z-filters and coz-ultrafilters

In this article we introduce the concepts of minimal prime z-filter, essential z-filter and r-filter. we investigate and study the behavior of minimal prime z-filters and compare them with minimal prime ideals and coz-ultrafilters. we show that x is a p-space if and only if every fixed prime z-filter is minimal prime. it is observed that if x is a ∂-space then x is a p-space if and only if z[mf ] is an r-filter, for every f ∈ c(x). the collection of all minimal prime z-filters will be topologized and it is proved that the space of minimal prime z-filters is homeomorphic with the space of coz-ultrafilters. finally, it is obtained several properties and relations between the space of minimal prime z-filters and the space of minimal prime ideals in c(x).