This research explores coz-filters in topological spaces and their connection to minimal prime ideals in the ring of continuous functions C(X). Coz-filters, associated with cozero sets, are examined in P-spaces and F-spaces to establish parallels with the well-studied z-ultrafilters and maximal ideals of C(X). By introducing a topological framework for coz-ltrafilters, we compare it with hull-kernel and inverse topologies. The study builds on existing literature on the relationship between C(X) and X, focusing on Tychonoff spaces and commutative rings. We investigate conditions under which minimal prime ideals correspond to coz-ultrafilters, explore homeomorphism conditions between X and the space of coz-ultrafilters, and analyze properties of coz-ultrafilters in lattice-ordered groups. This research aims to deepen understanding of the structural and topological characteristics of coz-filters in relation to continuous functions and topological spaces .
