A topological approach to Best Approximation Theory
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2004-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1994 |
| _version_ | 1818303640601886720 |
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| author | Samuel G. Moreno Jose María Almira Esther M. García-Caballero J.M. Quesada |
| author_facet | Samuel G. Moreno Jose María Almira Esther M. García-Caballero J.M. Quesada |
| author_sort | Samuel G. Moreno |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T05:58:01Z |
| format | Article |
| id | doaj.art-27d7aecbe6264e40bb54d36d8a1db53b |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-13T05:58:01Z |
| publishDate | 2004-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-27d7aecbe6264e40bb54d36d8a1db53b2022-12-21T23:57:24ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472004-04-0151497010.4995/agt.2004.19941616A topological approach to Best Approximation TheorySamuel G. Moreno0Jose María Almira1Esther M. García-Caballero2J.M. Quesada3Universidad de JaénUniversidad de JaénUniversidad de JaénUniversidad de JaénThe 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.http://polipapers.upv.es/index.php/AGT/article/view/1994WrappingBest ApproximationProximinalityCompactness |
| spellingShingle | Samuel G. Moreno Jose María Almira Esther M. García-Caballero J.M. Quesada A topological approach to Best Approximation Theory Applied General Topology Wrapping Best Approximation Proximinality Compactness |
| title | A topological approach to Best Approximation Theory |
| title_full | A topological approach to Best Approximation Theory |
| title_fullStr | A topological approach to Best Approximation Theory |
| title_full_unstemmed | A topological approach to Best Approximation Theory |
| title_short | A topological approach to Best Approximation Theory |
| title_sort | topological approach to best approximation theory |
| topic | Wrapping Best Approximation Proximinality Compactness |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1994 |
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