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

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 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

References

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Published

2019-10-01

How to Cite

[1]
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.

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Articles