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

0506888 - MÚ 2020 RIV PL eng J - Journal Article
Cúth, M. - Kurka, Ondřej - Vejnar, B.
Large separated sets of unit vectors in Banach spaces of continuous functions.
Colloquium Mathematicum. Roč. 157, č. 2 (2019), s. 173-187. ISSN 0010-1354. E-ISSN 1730-6302
Institutional support: RVO:67985840
Keywords : Banach space * nonseparable space
OECD category: Pure mathematics
Impact factor: 0.535, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.4064/cm7648-1-2019

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 . We prove that this is the case if the density is at most gamma, 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.
Permanent Link: http://hdl.handle.net/11104/0298018