Large separated sets of unit vectors in Banach spaces of continuous functions

Abstract

The paper concerns the problem whether a nonseparable $\C(K)$ space must contain a set of unit vectors whose cardinality equals to the density of $\C(K)$ such that the distances between every two distinct vectors are always greater than one. We prove that this is the case if the density is at most continuum and we prove that for several classes of $\C(K)$ spaces (of arbitrary density) it is even possible to find such a set which is $2$-equilateral; that is, the distance between every two distinct vectors is exactly 2.

arXiv commentThe second version does not contain new results, but it is reorganized in order to distinguish our main contributions from what was essentially known

Cited by in corpus (1)

• Separated sets and Auerbach systems in Banach spaces