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Title

On strong proximinality in normed linear spaces

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Abstract

The paper deals with strong proximinality in normed linear spaces. It is proved that in  a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and  approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed.

Keywords

ENG
Strongly proximinal set, approximatively compact set, strongly Chebyshev set, compactly locally uniformly rotund space

Bibliography

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Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
2016/70/1
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Main language of publication
English
Published
2016
Published online
2016-07-04

DOI: 10.17951/a.2016.70.1.19

Exact and natural sciences