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

Colloquium Mathematicum MSC: Primary 46B20, 46B04, 46E15; Secondary 54D30, 46B26. DOI: 10.4064/cm7648-1-2019 Opublikowany online: 8 April 2019

#### Streszczenie

The paper concerns the problem of whether a nonseparable $\mathcal {C}(K)$ space must contain a set of unit vectors whose cardinality equals the density of $\mathcal {C}(K)$, 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 $\mathfrak {c}$, and that for several classes of $\mathcal {C}(K)$ 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.

#### Autorzy

• Marek CúthCharles University
Faculty of Mathematics and Physics
Department of Mathematical Analysis
Sokolovská 83
186 75 Praha 8, Czech Republic
e-mail
• Ondřej KurkaCharles University
Faculty of Mathematics and Physics
Department of Mathematical Analysis
Sokolovská 83
186 75 Praha 8, Czech Republic
and
Institute of Mathematics
Žitná 25
115 67 Praha 1, Czech Republic
e-mail
• Benjamin VejnarCharles University
Faculty of Mathematics and Physics
Department of Mathematical Analysis
Sokolovská 83
186 75 Praha 8, Czech Republic
e-mail

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