On embedding separable spaces C ( L ) in arbitrary spaces C ( K ).

IF 1.1 2区数学 Q1 MATHEMATICS

Banach Journal of Mathematical Analysis Pub Date : 2025-01-01 Epub Date: 2025-07-09 DOI:10.1007/s43037-025-00439-0

Jakub Rondoš, Damian Sobota

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引用次数: 0

Abstract

Supplementing and expanding classical results, for compact spaces K and L, L metric, and their Banach spaces $C (L)$ and $C (K)$ of continuous real-valued functions, we provide several characterizations of the existence of isometric, resp. isomorphic, embeddings of $C (L)$ into $C (K)$ . In particular, we show that if the embedded space $C (L)$ is separable, then the classical theorems of Holsztyński and Gordon become equivalences. We also obtain new results describing the relative cellularities of the perfect kernel of a given compact space K and of the Cantor-Bendixson derived sets of K of countable order in terms of the presence of isometric copies of specific spaces $C (L)$ inside $C (K)$ .

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关于在任意空间C (K)中嵌入可分离空间C (L)的问题。

补充和扩展了经典结果，对于连续实值函数的紧化空间K和L， L度量，以及它们的Banach空间C (L)和C (K)，我们给出了等距的存在性的几个表征。同构，C (L)嵌入C (K)。特别地，我们证明了如果嵌入空间C (L)是可分的，那么Holsztyński的经典定理和Gordon的经典定理成为等价的。我们还获得了新的结果，描述了给定紧空间K的完美核的相对胞性，以及在C (K)内存在特定空间C (L)的等距副本的康托-本迪克森导出的K的可数阶集的相对胞性。

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

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.