Ideal spaces

Authors

DOI:

https://doi.org/10.4995/agt.2021.13608

Keywords:

rings of continuous functions, CK(X) and C∞(X), nearly pseudocompact spaces, RCC properties

Abstract

Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X). We define those spaces X to be ideal space where C∞ (X) is an ideal of C(X). We have proved that nearly pseudocompact spaces are ideal spaces. For the converse, we introduced a property called “RCC” property and showed that an ideal space X is nearly pseudocompact if and only if X satisfies ”RCC” property. We further discussed some topological properties of ideal spaces.

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Author Biographies

Biswajit Mitra, University of Burdwan

Assistant ProfessorDepartment of Mathematics

Debojyoti Chowdhury, University of Burdwan

Research ScholarDepartment of Mathematics

References

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Published

2021-04-01

How to Cite

[1]
B. Mitra and D. Chowdhury, “Ideal spaces”, Appl. Gen. Topol., vol. 22, no. 1, pp. 79–89, Apr. 2021.

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