Discrete Open and Closed Mappings on Generalized Continua and Newman's Property

McAuley, Louis F. ; Robinson, Eric E.

Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 1081-1112

Résumé

In 1930, M. H. A. Newman proved a rather remarkable theorem which has become one of the classical theorems in topology. It has many important applications. A special case of Newman's Theorem is that a periodic homeomorphism of period n > 1 of a sphere S onto itself must have some orbit which is not contained in a “cap” smaller than a hemisphere. The general theorem is as follows:THEOREM ([15]). Suppose that Mn is a connected (metric) n-manifold, U is a domain in Mn, andp is an integer greater than 1. Then there is a positive number d such that no uniformly continuous homeomorphism h of Mn onto itself of period p moves every point of U a distance < d. That is, there is x ∊ U so that the orbit of x under h has diameter ≦ d.

Détail

DOI : 10.4153/CJM-1984-062-9

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