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 2 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). [ABSTRACT FROM AUTHOR]