ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)

Amir Veisi

Abstract

The purpose of this article is to study and investigate ec-filters on X and ec-ideals in C*c (X) in which they are in fact the counterparts of zc-filters on X and zc-ideals in Cc(X) respectively. We show that the maximal ideals of C*c (X) are in one-to-one correspondence with the ec-ultrafilters on X. In addition, the sets of ec-ultrafilters and zc-ultrafilters are in one-to-one correspondence. It is also shown that the sets of maximal ideals of Cc(X) and C*c (X) have the same cardinality. As another application of the new concepts, we characterized maximal ideals of C*c (X). Finally, we show that whether the space X is compact, a proper ideal I of Cc(X) is an ec-ideal if and only if it is a closed ideal in Cc(X) if and only if it is an intersection of maximal ideals of Cc(X).


Keywords

c-completely regular space; closed ideal; functionally countable space; ec-filter; ec-ideal; zero-dimensional space

Subject classification

54C30; 54C40; 54C05; 54G12; 13C11; 16H20.

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