Nonseparable C(K)-spaces can be twisted when K is a finite height compact

2016/01/08 by Jesús M. F. Castillo, Castillo, Jesús M. F.
Computer Science · Mathematics · #46B20 #46B25 #46M18 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B20 #msc:46B25 #msc:46M18

paper · pdf · doi:10.48550/arxiv.1601.02037

To appear in Topology and Applications

arxiv created 2016/01/08 · openalex publication_date 2016/01/08 · arxiv updated 2016/01/12 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

We show that, given a nonmetrizable compact space K having ω-derived set empty, there always exist nontrivial exact sequences 0→ c₀→ E→ C(K)→ 0. This partially solves a problem posed in several papers: Is Ext(C(K), c₀)≠ 0 for K a nonmetrizable compact set?

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