Characterisations of Chebyshev sets in c0 |
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Authors: | Alexey R Alimov |
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Institution: | Department of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119992, Russia |
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Abstract: | A subset MX of a normed linear space X is a Chebyshev set if, for every xX, the set of all nearest points from M to x is a singleton. We obtain a geometrical characterisation of approximatively compact Chebyshev sets in c0. Also, given an approximatively compact Chebyshev set M in c0 and a coordinate affine subspace Hc0 of finite codimension, if M∩H≠, then M∩H is a Chebyshev set in H, where the norm on H is induced from c0. |
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Keywords: | Chebyshev set Sun c0 |
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