标题： 阿斯普伦德空间 $C_k(X)$ 超过巴拿赫空间 显示英文标题

标题： Asplund spaces $C_k(X)$ beyond Banach spaces

摘要： 本文讨论了当$X$是任意的Tychonoff空间时，赋以紧致-开拓扑的连续函数空间$C_k(X)$的Asplund性质。 受先验文献中关于将Asplund性质扩展到巴拿赫空间之外的不一致定义的启发，我们在此背景下提供了核心结果的统一且自洽的处理。 建立了$C_k(X)$的Asplund性质的特征，同时回顾了经典结果，包括Namioka--Phelps定理及其影响。 所有证明均以自洽的方式呈现，并依赖于标准技术。 显示英文摘要

摘要： 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.