Ideal spaces

Biswajit Mitra, Debojyoti Chowdhury

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.


Keywords

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

Subject classification

54F65; 54G20; 54D45; 54D60; 54D99.

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Universitat Politècnica de València

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