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The character of free topological groups I

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The character of free topological groups I

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dc.contributor.author Nickolas, Peter es_ES
dc.contributor.author Tkachenko, Mikhail es_ES
dc.date.accessioned 2017-06-09T07:23:37Z
dc.date.available 2017-06-09T07:23:37Z
dc.date.issued 2005-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/82621
dc.description.abstract [EN] A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself. From these results, others follow on the basis of various topological assumptions. Amongst these: (i) if X is a compact Hausdorff space, then the character of the free abelian topological group on X lies between w(X) and w(X)ℵ0, where w(X) denotes the weight of X; (ii) if the Tychonoff space X is not a P-space, then the character of the free abelian topological group is bounded below by the “small cardinal” d; and (iii) if X is an infinite compact metrizable space, then the character is precisely d. In the non-abelian case, we show that the character of the free abelian topological group is always less than or equal to that of the corresponding free topological group, but the inequality is in general strict. It is also shown that the characters of the free abelian and the free topological groups are equal whenever the given uniform space is w-narrow. A sequel to this paper analyses more closely the cases of the free and free abelian topological groups on compact Hausdorff spaces and metrizable spaces. es_ES
dc.description.sponsorship The first author wishes to thank the second author, and his department, for hospitality extended during the course of this work. The second author was supported by Mexican National Council of Sciences and Technology (CONACyT), Grant No. 400200-5-28411-E.
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation CONACYT/400200-5-28411-E
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Free (abelian) topological group es_ES
dc.subject Uniform space es_ES
dc.subject Entourage of the diagonal es_ES
dc.subject Character es_ES
dc.subject Cardinal invariant es_ES
dc.subject Compact es_ES
dc.subject Locally compact es_ES
dc.subject Pseudocompact es_ES
dc.subject Metrizable es_ES
dc.subject kω-space es_ES
dc.subject Dominating family es_ES
dc.subject.classification 56 es_ES
dc.title The character of free topological groups I es_ES
dc.type Artículo es_ES
dc.date.updated 2017-06-09T06:18:37Z
dc.identifier.doi 10.4995/agt.2005.1961
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Nickolas, P.; Tkachenko, M. (2005). The character of free topological groups I. Applied General Topology. 6(1):43-46. doi:10.4995/agt.2005.1961. es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2005.1961 es_ES
dc.description.upvformatpinicio 43
dc.description.upvformatpfin 46 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 6
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.contributor.funder Consejo Nacional de Ciencia y Tecnología, México


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