Ideal spaces

• Mitra, Biswajit ^[1] ; Chowdhury, Debojyoti ^[1]
  1. [1] University of Burdwan
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 1, 2021, págs. 79-89
• Idioma: inglés
• DOI: 10.4995/agt.2021.13608
• Enlaces
  • Texto completo
• Resumen

  • 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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