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Generating continuous mappings with Lipschitz mappings
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dc.contributor.author | Cichon, J | |
dc.contributor.author | Mitchell, James David | |
dc.contributor.author | Morayne, M | |
dc.date.accessioned | 2010-12-03T12:30:02Z | |
dc.date.available | 2010-12-03T12:30:02Z | |
dc.date.issued | 2007-05 | |
dc.identifier.citation | Cichon , J , Mitchell , J D & Morayne , M 2007 , ' Generating continuous mappings with Lipschitz mappings ' , Transactions of the American Mathematical Society , vol. 359 , no. 5 , pp. 2059-2074 . https://doi.org/10.1090/S0002-9947-06-04026-8 | en |
dc.identifier.issn | 0002-9947 | |
dc.identifier.other | PURE: 254893 | |
dc.identifier.other | PURE UUID: a55dd3c0-e48c-4ea1-86fe-bc2ddf5d8309 | |
dc.identifier.other | WOS: 000243610400006 | |
dc.identifier.other | Scopus: 34247474140 | |
dc.identifier.other | ORCID: /0000-0002-5489-1617/work/73700789 | |
dc.identifier.uri | https://hdl.handle.net/10023/1616 | |
dc.description.abstract | If X is a metric space, then C-X and L-X denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of C-X modulo L-X is the least cardinality of any set U\L-X where U generates C-X. For a large class of separable metric spaces X we prove that the relative rank of C-X modulo L-X is uncountable. When X is the Baire space N-N, this rank is N-1. A large part of the paper emerged from discussions about the necessity of the assumptions imposed on the class of spaces from the aforementioned results. | |
dc.format.extent | 16 | |
dc.language.iso | eng | |
dc.relation.ispartof | Transactions of the American Mathematical Society | en |
dc.rights | (c)2007 American Mathematical Society. First published in Transactions of the American Mathematical Society 359 (2007), available at http://www.ams.org | en |
dc.subject | Relative ranks | en |
dc.subject | Functions spaces | en |
dc.subject | Continuous mappings | en |
dc.subject | Lipschitz mappings | en |
dc.subject | Baire space | en |
dc.subject | Transformation semigroups | en |
dc.subject | Ranks | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Generating continuous mappings with Lipschitz mappings | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1090/S0002-9947-06-04026-8 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=34247474140&partnerID=8YFLogxK | en |
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