#### Vol. 301, No. 2, 2019

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New applications of extremely regular function spaces

### Trond A. Abrahamsen, Olav Nygaard and Märt Põldvere

Vol. 301 (2019), No. 2, 385–394
DOI: 10.2140/pjm.2019.301.385
##### Abstract

Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of ${C}_{0}\left(L\right)$ have very strong diameter $2$ properties and, for every real number $\epsilon$ with $0<\epsilon <1$, contain an $\epsilon$-isometric copy of ${c}_{0}$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of ${\ell }_{1}$.

##### Keywords
extremely regular function space, strong diameter 2 property, almost square space, octahedrality, Daugavet property
##### Mathematical Subject Classification 2010
Primary: 46B20, 46B22, 46B04
##### Milestones
Received: 2 November 2017
Revised: 25 September 2018
Accepted: 9 December 2018
Published: 24 October 2019
##### Authors
 Trond A. Abrahamsen Department of Mathematics University of Agder Kristiansand Norway Olav Nygaard Department of Mathematics University of Agder Kristiansand Norway Märt Põldvere Institute of Mathematics and Statistics University of Tartu Tartu Estonia