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Centralizers of rank-one homeomorphisms

Published online by Cambridge University Press:  03 December 2012

AARON HILL*
Affiliation:
Mathematics, University of North Texas, Denton, USA (email: [email protected])

Abstract

We give a definition for a rank-one homeomorphism of a zero-dimensional Polish space X. We show that if a rank-one homeomorphism of X satisfies a certain non-degeneracy condition, then it has trivial centralizer in the group of all homeomorphisms of X, i.e. it commutes only with its integral powers.

Type
Research Article
Copyright
©2012 Cambridge University Press 

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