Generating continuous mappings with Lipschitz mappings

J Cichon, James David Mitchell, M Morayne

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2059-2074
Number of pages16
JournalTransactions of the American Mathematical Society
Volume359
Issue number5
DOIs
Publication statusPublished - May 2007

Keywords

  • Relative ranks
  • Functions spaces
  • Continuous mappings
  • Lipschitz mappings
  • Baire space
  • Transformation semigroups
  • Ranks

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