Bhattacharjee, P., M. Drees, K. (2017). Filters of Coz(X). Categories and General Algebraic Structures with Applications, 7(Special Issue on the Occasion of Banaschewski's 90th Birthday (II)), 107-123.

Papiya Bhattacharjee; Kevin M. Drees. "Filters of Coz(X)". Categories and General Algebraic Structures with Applications, 7, Special Issue on the Occasion of Banaschewski's 90th Birthday (II), 2017, 107-123.

Bhattacharjee, P., M. Drees, K. (2017). 'Filters of Coz(X)', Categories and General Algebraic Structures with Applications, 7(Special Issue on the Occasion of Banaschewski's 90th Birthday (II)), pp. 107-123.

Bhattacharjee, P., M. Drees, K. Filters of Coz(X). Categories and General Algebraic Structures with Applications, 2017; 7(Special Issue on the Occasion of Banaschewski's 90th Birthday (II)): 107-123.

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

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

Abstract

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.

Highlights

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

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