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Generating continuous mappings with Lipschitz mappings

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Mitchell2007_AmerMathSoc359_Generating.pdf (248.3Kb)
Date
05/2007
Author
Cichon, J
Mitchell, James David
Morayne, M
Keywords
Relative ranks
Functions spaces
Continuous mappings
Lipschitz mappings
Baire space
Transformation semigroups
Ranks
QA Mathematics
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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.
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
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1090/S0002-9947-06-04026-8
ISSN
0002-9947
Type
Journal article
Rights
(c)2007 American Mathematical Society. First published in Transactions of the American Mathematical Society 359 (2007), available at http://www.ams.org
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  • University of St Andrews Research
URL
http://www.scopus.com/inward/record.url?scp=34247474140&partnerID=8YFLogxK
URI
http://hdl.handle.net/10023/1616

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