Two New Examples of Sets without Medians and Centers

• Autores: Pier Luigi Papini
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 13, Nº. 2, 2005, págs. 315-320
• Idioma: inglés
• DOI: 10.1007/bf02579057
• Texto completo no disponible (Saber más ...)
• Resumen

  • Many problems in continuous location theory, reduce to finding a best location, in the sense that a facility must be located at a point minimizing the sum of distances to the points of a given finite set (median) or the largest distances to all points (center). The setting is often assumed to be a Banach space. To have a better understanding concerning the structure of location problems, it is nice to see how, if the space is infinite-dimensional, the lack of optimal solutions may occur also in rather simple cases. In this paper we indicate two simple examples of four-point sets such that one of the two problems indicated has a solution, while the other one has no solution. Also, we list papers containing examples previously given, dealing with this lack of optimal solutions.