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arXiv 2009.07902math.GNmath.FA
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利用收缩骨架表征(半)Eberlein Escherta

Characterization of (semi-)Eberlein compacta using retractional skeletons

Claudia Correa, Marek Cúth, Jacopo Somaglia

摘要:

我们深入地研究了与合适的模型在紧空间承认一个收缩骨架的收缩,并发现了几个有趣的后果。最重要的是,我们提供了一个新的表征Valdivia lutta使用的概念,回缩骨架,这似乎是有帮助的特征时,其子类。此外,我们的特点Eberlein和半Eberlein Eberlein Eberta的收缩骨架,并表明,我们的新的特征给出了另一种证明的事实,即连续图像的Eberlein紧以及新的稳定性结果的类半Eberlein Eberlein Eberta,特别是解决了一个公开的问题所提出的Kubis和Leiderman。

英文摘要:

We deeply study retractions associated to suitable models in compact spaces admitting a retractional skeleton and find several interesting consequences. Most importantly, we provide a new characterization of Valdivia compacta using the notion of retractional skeletons, which seems to be helpful when characterizing its subclasses. Further, we characterize Eberlein and semi-Eberlein compacta in terms of retractional skeletons and show that our new characterizations give an alternative proof of the fact that continuous image of an Eberlein compact is Eberlein as well as new stability results for the class of semi-Eberlein compacta, solving in particular an open problem posed by Kubis and Leiderman.

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