A topological approach to Best Approximation Theory

  1. Moreno, Samuel G. 1
  2. Almira, Jose María 1
  3. García-Caballero, Esther M. 1
  4. Quesada, J.M. 1
  1. 1 Universidad de Jaén
    info

    Universidad de Jaén

    Jaén, España

    ROR https://ror.org/0122p5f64

Revista:
Applied general topology

ISSN: 1576-9402,  1989-4147

Año de publicación: 2004

Volumen: 5

Número: 1

Páginas: 49-70

Tipo: Artículo

DOI: 10.4995/AGT.2004.1994 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Applied general topology

Objetivos de desarrollo sostenible

Resumen

The main goal of this paper is to put some light in several arguments that have been used through the time in many contexts of Best Approximation Theory to produce proximinality results. In all these works, the main idea was to prove that the sets we are considering have certain properties which are very near to the compactness in the usual sense. In the paper we introduce a concept (the wrapping) that allow us to unify all these results in a whole theory, where certain ideas from Topology are essential. Moreover, we do not only cover many of the known classical results but also prove some new results. Hence we prove that exists a strong interaction between General Topology and Best Approximation Theory.

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