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Large separated sets of unit vectors in Banach spaces of continuous functions
Type of publication: Article
Citation:
Publication status: Published
Journal: Colloquium Mathematicum
Volume: 157
Number: 2
Year: 2019
Pages: 173--187
URL: https://www.impan.pl/pl/wydawn...
DOI: 10.4064/cm7648-1-2019
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.
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Authors Cúth, Marek
Kurka, Ondřej
Vejnar, Benjamin
Added by: [mc]
Total mark: 0
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