A topological approach to Best Approximation Theory


  • Samuel G. Moreno Universidad de Jaén
  • Jose María Almira Universidad de Jaén
  • Esther M. García-Caballero Universidad de Jaén
  • J.M. Quesada Universidad de Jaén




Wrapping, Best Approximation, Proximinality, Compactness


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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Author Biographies

Samuel G. Moreno, Universidad de Jaén

Departamento de Matemáticas

Jose María Almira, Universidad de Jaén

Departamento de Matemáticas

Esther M. García-Caballero, Universidad de Jaén

Departamento de Matemáticas

J.M. Quesada, Universidad de Jaén

Departamento de Matemáticas


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How to Cite

S. G. Moreno, J. M. Almira, E. M. García-Caballero, and J. Quesada, “A topological approach to Best Approximation Theory”, Appl. Gen. Topol., vol. 5, no. 1, pp. 49–70, Apr. 2004.



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