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


  • Amir Veisi Yasouj University



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


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).


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Author Biography

Amir Veisi, Yasouj University

Faculty of Petroleum and Gas


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How to Cite

A. Veisi, “ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)”, Appl. Gen. Topol., vol. 20, no. 2, pp. 395–405, Oct. 2019.