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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 735582
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Abstract: 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 $ \hat H(P)$ of maps of the pseudo-arc into itself which are homeomorphisms onto their images is a dense $ {G_\delta }$ in $ M(P)$. (2) Every homeomorphism of the pseudo-arc onto itself is a product of $ \in $-homeomorphisms. (3) There exists a nonidentity homeomorphism of the pseudo-arc with an infinite sequence of $ p$th roots. (4) Every map between chainable continua can be lifted to a homeomorphism of pseudo-arcs.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0735582-4
PII: S 0002-9939(1984)0735582-4
Keywords: Pseudo-arc, chainable continuum, $ \in $-homeomorphism, space of homeomorphisms
Article copyright: © Copyright 1984 American Mathematical Society