Most maps of the pseudo-arc are homeomorphisms

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We prove the following results. (1) If M(P) is the space of maps of the pseudo-arc into itself with the sup metric, then the subset H(P) of maps of the pseudo-arc into itself which are homeomorphisms onto their images is a dense Gs in M(P). (2) Every homeomorphism of the pseudo-arc onto itself is a product of e-homeomorphisms. (3) There exists a nonidentity homeomorphism of the pseudo-arc with an infinite sequence of pth roots. (4) Every map between chainable continua can be lifted to a homeomorphism of pseudo-arcs.

Original languageEnglish
Pages (from-to)147-154
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - May 1984


  • Chainable continuum
  • Pseudo-arc
  • Space of homeomorphisms
  • ε-homeomorphism


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