Abstract
The main existence theorem of this chapter states that every approximatively compact set is proximinal. This result contains virtually all the existence theorems of interest. In particular, the two most useful existence and uniqueness theorems can be deduced from it. They are: (1) Every finite-dimensional subspace is Chebyshev, and (2) every closed convex subset of a Hilbert space is Chebyshev.
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© 2001 Springer-Verlag New York, Inc.
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Deutsch, F. (2001). Existence and Uniqueness of Best Approximations. In: Best Approximation in Inner Product Spaces. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9298-9_3
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DOI: https://doi.org/10.1007/978-1-4684-9298-9_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2890-0
Online ISBN: 978-1-4684-9298-9
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