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A Note on Relatively Injective $$C_0(S)$$ -Modules $$C_0(S)$$
Functional Analysis and Its Applications ( IF 0.4 ) Pub Date : 2022-03-17 , DOI: 10.1134/s0016266321040043 N. T. Nemesh
中文翻译:
关于相对内射 $$C_0(S)$$ -Modules $$C_0(S)$$ 的注解
更新日期:2022-03-17
Functional Analysis and Its Applications ( IF 0.4 ) Pub Date : 2022-03-17 , DOI: 10.1134/s0016266321040043 N. T. Nemesh
Abstract
In this note we discuss some necessary and some sufficient conditions for the relative injectivity of the \(C_0(S)\)-module \(C_0(S)\), where \(S\) is a locally compact Hausdorff space. We also give a Banach module version of Sobczyk’s theorem. The main result of the paper is as follows: if the \(C_0(S)\)-module \(C_0(S)\) is relatively injective, then \(S=\beta(S\setminus \{s\})\) for any limit point \(s\in S\).
中文翻译:
关于相对内射 $$C_0(S)$$ -Modules $$C_0(S)$$ 的注解
摘要
在本笔记中,我们讨论了\(C_0(S)\) -模块\(C_0(S)\)的相对单射性的一些必要和充分条件,其中\(S\)是局部紧致 Hausdorff 空间。我们还给出了 Sobczyk 定理的 Banach 模块版本。论文的主要结果如下:如果\(C_0(S)\)-模\(C_0(S)\)是相对单射的,则\(S=\beta(S\setminus \{s\} )\)对于任何限制点\(s\in S\)。