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Small Compact Actions on Chainable Continua

Published online by Cambridge University Press:  20 November 2018

Juan A. Toledo
Juan A. Toledo*
Affiliation:
Universidad Autónoma Metropolitana – Iztapalapa, México, México
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1. Introduction. In 1931, Newman [9] showed that a connected manifold cannot accept arbitrarily small period-n homeomorphisms, for any n > 1. In this paper we are concerned with the existence of chainable continua with arbitrarily small homeomorphisms.

For a long time the only known periodic homeomorphisms of chainable continua had periods 1, 2 or 4 [4]. Recently, Wayne Lewis [8] showed that the pseudo-arc admits periodic homeomorphisms of every order, as well as p-adic cantor group actions. We will see that such homeomorphisms can be made arbitrarily small.

In Section 4, a different chainable indecomposable continuum accepting arbitrarily small period-2 homeomorphisms is constructed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 3 , 01 June 1986 , pp. 563 - 575
Copyright
Copyright © Canadian Mathematical Society 1986

References

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