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arXiv · 2610.05846

The renorming-stable ball covering property and $C(K)$-spaces

Rui Liu·Jie Shen·Richard J. Smith
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Abstract

A Banach space has the ball-covering property (BCP) if its unit sphere can be covered by countably many balls that miss the origin. A Banach space has the renorming-stable ball-covering property (RBCP) if it has the BCP with respect to every equivalent norm. We investigate the RBCP from the perspective of $C(K)$-spaces. In particular, we show that there are many non-separable $C(K)$-spaces having the RBCP. This yields an emphatic negative answer to a question of Cheng, Kato and Zhang from 2020.

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Rui Liu, Jie Shen, Richard J. Smith. 2026-10-05. The renorming-stable ball covering property and $C(K)$-spaces. https://arxiv.org/abs/2610.05846

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