Ideal spaces

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-04-01 DOI:10.4995/agt.2021.13608

B. Mitra, Debojyoti Chowdhury

引用次数: 5

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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理想的空间

设C∞(X)表示在无穷远处消失的实值连续函数族，使得{X∈X: |f(X) |≥1/n}在X上紧致，对于所有n∈n, C∞(X)是C(X)的理想，一般不成立。我们定义这些空间X为理想空间，其中C∞(X)是C(X)的理想。我们证明了近伪紧空间是理想空间。相反，我们引入了“RCC”性质，并证明了理想空间X是近似伪紧的当且仅当X满足“RCC”性质。进一步讨论了理想空间的一些拓扑性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.