Hyperspaces of a weightable quasi-metric space: Application to models in the theory of computation

It is well known that both weightable quasi-metrics and the Hausdorff distance provide efficient tools in several areas of Computer Science. This fact suggests, in a natural way, the problem of when the upper and lower Hausdorff quasi-pseudo-metrics of a weightable quasi-metric space (X,d) are weigh...

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Detalles Bibliográficos
Autores: Künzi, H.P.A., Rodríguez López, Jesús|||0000-0001-5141-9977, Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:español
OAI Identifier:oai:riunet.upv.es:10251/62310
Acceso en línea:https://riunet.upv.es/handle/10251/62310
Access Level:acceso abierto
Palabra clave:Weightable quasi-metric
Hausdorff quasi-pseudo-metric
Pompéiu quasi-pseudo-metric
Hyperspace
The specialization order
The information order
MATEMATICA APLICADA
Descripción
Sumario:It is well known that both weightable quasi-metrics and the Hausdorff distance provide efficient tools in several areas of Computer Science. This fact suggests, in a natural way, the problem of when the upper and lower Hausdorff quasi-pseudo-metrics of a weightable quasi-metric space (X,d) are weightable. Here we discuss this problem. Although the answer is negative in general, we show, however, that it is positive for several nice classes of (nonempty) subsets of X. Since the construction of these classes depends, to a large degree, on the specialization order of the quasi-metric d, we are able to apply our results to some distinguished quasi-metric models that appear in theoretical computer science and information theory, like the domain of words, the interval domain and the complexity space.