Filters of Coz(X)

    In this article we investigate filters of cozero sets for real-valued continuous functions, called coz-filters. Much is known for z-ultrafilters and their correspondence with maximal ideals of C(X).  Similarly, a correspondence will be established between coz-ultrafilters and minimal prime ideals of C(X).  We will further notice various properties of coz-ultrafilters in relation to P-spaces and  F-spaces.  In the last two sections, the collection of coz-ultrafilters will be topologized, and then compared to the hull-kernel and the inverse topologies placed on the collection of minimal prime ideals of C(X) and general lattice-ordered groups.

کلیدواژه ها:

Cozero sets ، ultrafilters ، minimal prime ideals ، P-space ، F-space ، inverse topology ، ell-groups