Ideal spaces
| Autor: | Biswajit Mitra, Debojyoti Chowdhury |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 22, Iss 1, Pp 79-89 (2021) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2021.13608 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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