Semadeni-Pełczyński derivative and functions on nonmetrizable cubes

2025/02/24 by Maciej Korpalski, Korpalski, Maciej
Mathematics · #46B03 #46E15 #54F05 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2502.16981

openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Banach spaces C(K) of real-valued continuous functions from the finite product of compact lines. It turns out that the topological character of these compact lines can be used to distinguish whether two spaces of continuous functions on products are isomorphic or embeddable to each other. In particular, for compact lines K₁, …, K_n, L₁, …, L_k of uncountable character and k ≠ n, we claim that Banach spaces C(∏_i=1ⁿ K_i) and C(∏_j=1^k L_j) are not isomorphic.

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