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dc.contributor.authorCichon, J.
dc.contributor.authorMitchell, James D.
dc.contributor.authorMorayne, Michal
dc.contributor.authorPeresse, Yann
dc.date.accessioned2017-04-20T16:00:39Z
dc.date.available2017-04-20T16:00:39Z
dc.date.issued2011-02-15
dc.identifier.citationCichon , J , Mitchell , J D , Morayne , M & Peresse , Y 2011 , ' Relative ranks of Lipschitz mappings on countable discrete metric spaces ' , Topology and its Applications , vol. 158 , no. 3 , pp. 412-423 . https://doi.org/10.1016/j.topol.2010.11.020
dc.identifier.issn0166-8641
dc.identifier.otherPURE: 10301417
dc.identifier.otherPURE UUID: 092180e7-6137-460c-9997-d06469171a60
dc.identifier.otherScopus: 78650716669
dc.identifier.urihttp://hdl.handle.net/2299/17993
dc.descriptionJ. Cichon, J. D. Mitchell, M. Morayne and Y. Peresse, 'Relative ranks of Lipschitz mappings on countable discrete metric spaces', Topology and its Applications, Vol. 158 (3): 412-423, first published online 3 December 2010. The version of record is available online at doi: https://doi.org/10.1016/j.topol.2010.11.020. Copyright © 2010 Elsever B. V. All rights reserved.
dc.description.abstractLet X be a countable discrete metric space and let XX denote the family of all functions on X. In this article, we consider the problem of finding the least cardinality of a subset A of XX such that every element of XX is a finite composition of elements of A and Lipschitz functions on X. It follows from a classical theorem of Sierpiński that such an A either has size at most 2 or is uncountable. We show that if X contains a Cauchy sequence or a sufficiently separated, in some sense, subspace, then |A|≤1. On the other hand, we give several results relating |A| to the cardinal d; defined as the minimum cardinality of a dominating family for NN. In particular, we give a condition on the metric of X under which |A|≥d holds and a further condition that implies |A|≤d. Examples satisfying both of these conditions include all subsets of Nk and the sequence of partial sums of the harmonic series with the usual euclidean metric. To conclude, we show that if X is any countable discrete subset of the real numbers R with the usual euclidean metric, then |A|=1 or almost always, in the sense of Baire category, |A|=d.en
dc.format.extent12
dc.language.isoeng
dc.relation.ispartofTopology and its Applications
dc.subjectrelative rank
dc.subjectfunction space
dc.subjectcontinuous mapping
dc.subjectLiptschitz mapping
dc.subjectSemigroups
dc.subjectdiscrete space
dc.titleRelative ranks of Lipschitz mappings on countable discrete metric spacesen
dc.contributor.institutionSchool of Physics, Astronomy and Mathematics
dc.description.statusPeer reviewed
rioxxterms.versionofrecordhttps://doi.org/10.1016/j.topol.2010.11.020
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


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