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When is an ultracomplete space almost locally compact?

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When is an ultracomplete space almost locally compact?

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dc.contributor.author Jardón Arcos, Daniel es_ES
dc.contributor.author Tkachuk, Vladimir V. es_ES
dc.date.accessioned 2017-06-16T09:44:13Z
dc.date.available 2017-06-16T09:44:13Z
dc.date.issued 2006-10-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/83018
dc.description.abstract [EN] We study spaces X which have a countable outer base in βX; they are called ultracomplete in the most recent terminology. Ultracompleteness implies Cech-completeness and is implied by almost local compactness (≡having all points of non-local compactness inside a compact subset of countable outer character). It turns out that ultracompleteness coincides with almost local compactness in most important classes of isocompact spaces (i.e., in spaces in which every countably compact subspace is compact). We prove that if an isocompact space X is ω-monolithic then any ultracomplete subspace of X is almost locally compact. In particular, any ultracomplete subspace of a compact ω-monolithic space of countable tightness is almost locally compact. Another consequence of this result is that, for any space X such that vX is a Lindelöf Σ-space, a subspace of Cp(X) is ultracomplete if and only if it is almost locally compact. We show that it is consistent with ZFC that not all ultracomplete subspaces of hereditarily separable compact spaces are almost locally compact. es_ES
dc.description.sponsorship Research supported by Consejo Nacional de Ciencia y Tecnología (CONACyT) of Mexico grants 94897 and 400200-5-38164-E.
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation CONACYT/94897 es_ES
dc.relation CONACYT/400200-5-38164-E
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Ultracompleteness es_ES
dc.subject Cech-completeness es_ES
dc.subject Countable type es_ES
dc.subject Pointwise countable type es_ES
dc.subject Lindelöf Σ-spaces es_ES
dc.subject Splittable spaces es_ES
dc.subject Eberlein compact spaces es_ES
dc.subject Almost locally compact spaces es_ES
dc.subject Isocompact spaces es_ES
dc.title When is an ultracomplete space almost locally compact? es_ES
dc.type Artículo es_ES
dc.date.updated 2017-06-16T08:57:28Z
dc.identifier.doi 10.4995/agt.2006.1923
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Jardón Arcos, D.; Tkachuk, VV. (2006). When is an ultracomplete space almost locally compact?. Applied General Topology. 7(2):191-201. doi:10.4995/agt.2006.1923. es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2006.1923 es_ES
dc.description.upvformatpinicio 191 es_ES
dc.description.upvformatpfin 201 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 7
dc.description.issue 2
dc.identifier.eissn 1989-4147
dc.contributor.funder Consejo Nacional de Ciencia y Tecnología, México


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