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Generating Continuous Mappings with Lipschitz Mappings
If X is a metric space then CX and LX denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of CX modulo LX is the least cardinality of any set U \LX where U generates CX . For a large class of separable metric spaces X we prove that the relative rank of CX modulo LX is uncountable. When X is the Baire space NN, this rank is א1. A large pa...
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ژورنال
عنوان ژورنال: International Journal of Fuzzy Logic and Intelligent Systems
سال: 2010
ISSN: 1598-2645
DOI: 10.5391/ijfis.2010.10.2.157