Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/8212
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Gutierres, Gonçalo | - |
dc.date.accessioned | 2009-02-09T14:22:39Z | - |
dc.date.available | 2009-02-09T14:22:39Z | - |
dc.date.issued | 2008 | en_US |
dc.identifier.citation | MLQ. 54:2 (2008) 145-152 | en_US |
dc.identifier.uri | https://hdl.handle.net/10316/8212 | - |
dc.description.abstract | Under the axiom of choice, every first countable space is a Fréchet-Urysohn space. Although, in its absence even R may fail to be a sequential space.Our goal in this paper is to discuss under which set-theoretic conditions some topological classes, such as the first countable spaces, the metric spaces, or the subspaces of R, are classes of Fréchet-Urysohn or sequential spaces.In this context, it is seen that there are metric spaces which are not sequential spaces. This fact raises the question of knowing if the completion of a metric space exists and it is unique. The answer depends on the definition of completion.Among other results it is shown that: every first countable space is a sequential space if and only if the axiom of countable choice holds, the sequential closure is idempotent in R if and only if the axiom of countable choice holds for families of subsets of R, and every metric space has a unique -completion. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) | en_US |
dc.language.iso | eng | eng |
dc.rights | openAccess | eng |
dc.title | On countable choice and sequential spaces | en_US |
dc.type | article | en_US |
dc.identifier.doi | 10.1002/malq.200710018 | en_US |
uc.controloAutoridade | Sim | - |
item.fulltext | Com Texto completo | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.languageiso639-1 | en | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
crisitem.author.dept | Faculty of Sciences and Technology | - |
crisitem.author.parentdept | University of Coimbra | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-9480-498X | - |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.