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Banach-Stone-like results for combinatorial Banach spaces
Annals of Pure and Applied Logic ( IF 0.6 ) Pub Date : 2021-04-28 , DOI: 10.1016/j.apal.2021.102989
C. Brech , C. Piña

We show that under a certain topological assumption on two compact hereditary families F and G on some infinite cardinal κ, the corresponding combinatorial spaces XF and XG are isometric if and only if there is a permutation of κ inducing a homeomorphism between F and G. We also prove that two different regular families F and G on ω cannot be permuted one to the other. Both these results strengthen the main result of [5].



中文翻译:

组合Banach空间的类似Banach-Stone的结果

我们表明,在一定的拓扑假设下,两个紧密的遗传家族 FG在一些无限基数κ上,对应的组合空间XFXG等轴测当且仅当存在κ的排列引起同构之间的同胚FG。我们还证明了两个不同的普通家庭FGω上不能彼此置换。这些结果都强化了[5]的主要结果。

更新日期:2021-05-04
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