TY  - JOUR
T1  - Large separated sets of unit vectors in Banach spaces of continuous functions
A1  - Cúth, Marek
A1  - Kurka, Ondřej
A1  - Vejnar, Benjamin
JA  - Colloquium Mathematicum
Y1  - 2019
VL  - 157
IS  - 2
SP  - 173
EP  - 187
UR  - https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/157/2/112965/large-separated-sets-of-unit-vectors-in-banach-spaces-of-continuous-functions
M2  - doi: 10.4064/cm7648-1-2019
N2  - 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.
ER  -