Original Articles

CONJUGACY CLASSES OF INVOLUTIONS IN THE GROUP OF HOMEOMORPHISMS OF THE RATIONAL NUMBERS

Published in: Quaestiones Mathematicae
Volume 24 , issue 2 , 2001 , pages: 237–246

DOI: 10.1080/16073606.2001.9639212

Author(s): P. V. Bruyns Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa,

Keywords: Rational numbers , conjugacy classes , involutions , fixed point sets

Abstract

Let X be the set of rational numbers Q with the topology induced by the usual topology on R and let AutX be the set of functions f: X → X which are homeomorphisms with respect to this topology. The set AutX is a group with respect to composition of functions. Let f ∊ AutX be an involution whose fixed point set has derived set with n elements. It is shown here that there are n + 2 conjugacy classes of such elements.

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