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

Amir Veisi

doi:10.4995/agt.2019.11524

Authors

Amir Veisi Yasouj University

DOI:

https://doi.org/10.4995/agt.2019.11524

Keywords:

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

Abstract

The purpose of this article is to study and investigate e_c-filters on X and e_c-ideals in C^*_c(X) in which they are in fact the counterparts of z_c-filters on X and z_c-ideals in C_c(X) respectively. We show that the maximal ideals of C^*_c(X) are in one-to-one correspondence with the e_c-ultrafilters on X. In addition, the sets of e_c-ultrafilters and z_c-ultrafilters are in one-to-one correspondence. It is also shown that the sets of maximal ideals of C_c(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 C_c(X) is an e_c-ideal if and only if it is a closed ideal in C_c(X) if and only if it is an intersection of maximal ideals of C_c(X).

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Author Biography

Amir Veisi, Yasouj University

Faculty of Petroleum and Gas

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