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arXiv · 2510.01873

Asplund spaces $C_k(X)$ beyond Banach spaces

Marian Fabian·Jerzy Kcakol·Arkady Leiderman
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Abstract

This paper addresses the Asplund property for the space of continuous functions $C_k(X)$ equipped with the compact-open topology, when $X$ is an arbitrary Tychonoff space. Motivated by inconsistent definitions in prior literature extending the Asplund property beyond Banach spaces, we provide a unified and self-contained treatment of core results in this context. A characterization of the Asplund property for $C_k(X)$ is established, alongside a review of classical results, including the Namioka--Phelps theorem and its implications. All proofs are presented in a self-contained manner and rely on standard techniques.

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Marian Fabian, Jerzy Kcakol, Arkady Leiderman. 2025-10-02. Asplund spaces $C_k(X)$ beyond Banach spaces. https://arxiv.org/abs/2510.01873

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