r-skeletons on the Alexandroff duplicate

2018/04/04 by S. Garcı́a-Ferreira, S. Garcia-Ferreira, Garcia-Ferreira, S. +2 · 1 citation
Mathematics · #54C15 #54D30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Holomorphic and Operator Theory #math.GN #msc:54C15 #msc:54D30

paper · pdf · doi:10.48550/arxiv.1804.01549

arxiv created 2018/04/04 · openalex publication_date 2018/04/04 · arxiv updated 2018/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An r-skeleton on a compact space is a family of continuous retractions having certain rich properties. The r-skeletons have been used to characterized the Valdivia compact spaces and the Corson compact spaces. Here, we characterized a compact space with an r-skeleton, for which the given r-skeleton can be extended to an r-skeleton on the Alexandroff Duplicate of the given space. Besides, we prove that if X is a zero-dimensional compact space without isolated points and \r_s:s∈ Γ\ is an r-skeleton on X, then there is s∈ Γ such that cl(r_s[X]) is not countable.

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• Families of retractions and families of closed subsets on compact spaces

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