On uniformly continuous surjections between function spaces

2024/03/31 by Ali Emre Eysen, Eysen, Ali Emre, Vesko Valov +1 · 1 citation
Mathematics · #54C35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2404.00542

openalex publication_date 2024/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider uniformly continuous surjections between C_p(X) and C_p(Y) (resp, C_p^*(X) and C_p^*(Y)) and show that if X has some dimensional-like properties, then so does Y. In particular, we prove that if T:C_p(X)→ C_p(Y) is a continuous linear surjection, then dim Y=0 if dim X=0. This provides a positive answer to a question raised by Kawamura-Leiderman \cite[Problem 3.1]kl.

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