Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Liu, Rui, Shen, Jie, Smith, Richard J.
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7991042
OpenAlex ID: W7220743509