Generating continuous mappings with Lipschitz mappings
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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.
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 . , 10.1090/S0002-9947-06-04026-8
Transactions of the American Mathematical Society
(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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