A Valdivia compact space with no G_δ points and few nontrivial convergent sequences

2015/06/05 by Claudia Correa, Correa, Claudia, Daniel V. Tausk +1
Mathematics · #46B20 #46E15 #54D30 #54F05 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46E15 #msc:54D30 #msc:54F05

paper · pdf · doi:10.48550/arxiv.1506.02077

The main part of this article has been merged with arXiv:1505.06727

openalex publication_date 2015/06/05 · arxiv created 2015/06/16 · arxiv updated 2015/06/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We give an example of a Valdivia compact space with no G_δ points and no nontrivial convergent sequences in the complement of a dense Σ-subset. The example is related to a problem concerning twisted sums of Banach spaces.

Citations

• Nontrivial twisted sums of c₀ and C(K)

Related

• Small Valdivia compacta and trees
• Convergent sequences in various topological spaces
• New examples of non-commutative Valdivia compact spaces
• Additional set-theoretic assumptions and twisted sums of Banach spaces
• On the class of continuous images of non-commutative Valdivia compacta