Equilateral sets in Banach spaces of the form $C(K)$
Volume 231 / 2015
Studia Mathematica 231 (2015), 241-255 MSC: Primary 46B20, 46E15; Secondary 46B26, 54D30. DOI: 10.4064/sm8259-1-2016 Published online: 17 February 2016
We show that for “most” compact nonmetrizable spaces, the unit ball of the Banach space $C(K)$ contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces $K$ such that the minimum cardinality of a maximal equilateral set in $C(K)$ is countable.