Applied General Topology - Vol 05, No 1 (2004)

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Iterated starcompact topological spaces
Representations of ordered semigroups and the Physical concept of Entropy
The topological structure of (homogeneous) spaces and groups with countable cs∗-character
A topological approach to Best Approximation Theory
Some problems on selections for hyperspace topologies
Star-Hurewicz and related properties
Homeomorphisms of R and the Davey Space
A countably compact free Abelian group whose size has countable cofinality
Continuous functions with compact support
Partial metrizability in value quantales
Fuzzy quasi-metric spaces

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A topological approach to Best Approximation Theory
(Universitat Politècnica de València, 2004-04-01) Moreno, Samuel G.; Almira, Jose María; García-Caballero, Esther M.; Quesada, J.M.; Junta de Andalucía
[EN] 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.