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

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.