Publication at Faculty of Mathematics and Physics |
2019
Abstract
The paper concerns the problem of whether a nonseparable C(K) space must contain a set of unit vectors whose cardinality equals the density of C(K), and such that the distances between any two distinct vectors are always greater than 1. We prove that this is the case if the density is at most c, and 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 two distinct vectors is exactly 2.