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All hypertopologies are hit-and-miss

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All hypertopologies are hit-and-miss

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dc.contributor.author Naimpally, Somashekhar es_ES
dc.date.accessioned 2017-05-30T10:46:59Z
dc.date.available 2017-05-30T10:46:59Z
dc.date.issued 2002-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/82018
dc.description.abstract [EN] We solve a long standing problem by showing that all known hypertopologies are hit-and-miss. Our solution is not merely of theoretical importance. This representation is useful in the study of comparison of the Hausdorff-Bourbaki or H-B uniform topologies and the Wijsman topologies among themselves and with others. Up to now some of these comparisons needed intricate manipulations. The H-B uniform topologies were the subject of intense activity in the 1960's in connection with the Isbell-Smith problem. We show that they are proximally locally finite topologies from which the solution to the above problem follows easily. It is known that the Wijsman topology on the hyperspace is the proximal ball (hit-and-miss) topology in”nice” metric spaces including the normed linear spaces. With the introduction of a new far-miss topology we show that the Wijsman topology is hit-and-miss for all metric spaces. From this follows a natural generalization of the Wijsman topology to the hyperspace of any T1 space. Several existing results in the literature are easy consequences of our work es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Hypertopology es_ES
dc.subject Vietoris topology es_ES
dc.subject Hausdorff metric es_ES
dc.subject Hausdorff-Bourbaki uniformity es_ES
dc.subject Uniformity es_ES
dc.subject Proximal topology es_ES
dc.subject Hit-and-miss topology es_ES
dc.subject Locally finite es_ES
dc.subject Wijsman topology es_ES
dc.subject Proximal ball topology es_ES
dc.subject Ball topology es_ES
dc.subject Far-miss topology es_ES
dc.subject Bounded Vietoris topology es_ES
dc.title All hypertopologies are hit-and-miss es_ES
dc.type Artículo es_ES
dc.date.updated 2017-05-30T09:28:11Z
dc.identifier.doi 10.4995/agt.2002.2111
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Naimpally, S. (2002). All hypertopologies are hit-and-miss. Applied General Topology. 3(1):45-53. doi:10.4995/agt.2002.2111 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2002.2111 es_ES
dc.description.upvformatpinicio 45 es_ES
dc.description.upvformatpfin 53 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 3
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.provenance Universitat Politècnica de València


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