The Coz-filters correspondence with ideals of C^*(X) (resp. C) on compact spaces

Abstract

This paper looks for the between filter-ideal connection of C^* (resp. C), on compact Tychonoff space (e.g.βX). The main matter of this work are cozero-set-filters connection and the prime ideal of C^* (X). examining coz-filters property on compact spaces (e.g. Stone–Čech compactification), we found a 1-1 relationship betwixt prime coz-filters and points of X, as long as analogue of the duality p↦M_p and maximal z-filter in C(X), and examine under which condition maximal coz-filters on βX correspond to points in C^* (X).  Confirming that the ideal-filters structures, founded in C(X), stay same in compact setting of C^* (X).