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Generating continuous mappings with Lipschitz mappings |
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| Authors: | J Cichon J D Mitchell M Morayne |
| Institution: | Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland ; Mathematics Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland ; Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland |
| Abstract: | If  is a metric space, then  and  denote the semigroups of continuous and Lipschitz mappings, respectively, from  to itself. The relative rank of  modulo  is the least cardinality of any set  where  generates  . For a large class of separable metric spaces  we prove that the relative rank of  modulo  is uncountable. When  is the Baire space  , this rank is  . 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. |
| Keywords: | Relative ranks functions spaces continuous mappings Lipschitz mappings Baire space |
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