By Vesely L.
Given a Banach spaceX, letc 0(X) be the distance of all null sequences inX (equipped with the supremum norm). We exhibit that: 1) every one compact set inc 0(X) admits a (Chebyshev) heart iff every one compact set inX admits a middle; 2) forX pleasing a undeniable situation (Q), each one bounded set inc 0(X) admits a middle iffX is quasi uniformly rotund. We build a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the (Q) andX isn't quasi uniformly rotund. It follows that the Banach spaceE=c 0(X) has the valuables from the name.
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Additional info for A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers
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Probably the most immediate applicability of genomic sequencing in clinical practice, in addition to reaching an accurate genetic diagnosis, is in the field of pharmacogenomics. 5 million SNVs and ~ 1000 CNVs on average in any given human diploid genome. Multiple bioinformatic prediction tools are available to aid in discerning deleterious from benign variation, based on parameters such as the conservation of an amino acid at a particular location across species and the biochemical properties of the reference versus variant amino acid.
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A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers by Vesely L.