Most maps of the pseudo-arc are homeomorphisms

Author:
Wayne Lewis

Journal:
Proc. Amer. Math. Soc. **91** (1984), 147-154

MSC:
Primary 54F20; Secondary 54H15

DOI:
https://doi.org/10.1090/S0002-9939-1984-0735582-4

MathSciNet review:
735582

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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0735582-4

Keywords:
Pseudo-arc,
chainable continuum,
-homeomorphism,
space of homeomorphisms

Article copyright:
© Copyright 1984
American Mathematical Society