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Restricted centers in $ C(\Omega )$


Authors: Philip W. Smith and J. D. Ward
Journal: Proc. Amer. Math. Soc. 48 (1975), 165-172
MSC: Primary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0380227-3
MathSciNet review: 0380227
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Abstract: The concept of restricted center is a natural generalization of the notion of Chebyshev center. We prove a necessary and sufficient condition for a bounded subset $ A$ of $ C(\Omega ),\Omega $ paracompact, to have a restricted center with respect to $ B$, another subset of $ C(\Omega )$. This theorem is then applied to subspaces of finite codimension in $ C(I),I$ a compact interval.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0380227-3
Keywords: Chebyshev center, best approximation, proximinal
Article copyright: © Copyright 1975 American Mathematical Society