2012/12/18 by G. Botelho, Geraldo Botelho, D. Cariello +12
Mathematics · #15A03 #26A15 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:15A03 #msc:26A15
paper · pdf · doi:10.48550/arxiv.1212.4395
arxiv created 2012/12/18 · openalex publication_date 2012/12/18 · arxiv updated 2012/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for functions defined on certain subsets of R are actually true for functions on quite general topological spaces. In the line of the original results of Gurariy and Quarta, we prove that, depending on the desired dimension, such subspaces may exist or not.