Filters of Coz(X)

Document Type : Research Paper


1 School of Science, Penn State Behrend, Erie, PA 16563, USA.

2 Department of Mathematics and Information Technology, Mercyhurst University, Erie PA.


    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.


Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday


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