Conjugate homeomorphisms of the Rational World
JOHN KENNETH TRUSS · Forum Mathematicum · 1997
Introduction If one considers the most familiar infinite permutation group, the full symmetric group Sym(\\Omega\\Gamma on an infinite set\\Omega\\Gamma it is very easy to give explicit descriptions (via cycle types) of the conjugacy classes of its elements. In other cases this is generally much harder, though some information can often be obtained, and for certain purposes can be quite illuminating. Holland gave an elegant classification of conjugacy in the automorphism group of any linearly ordered set (see [2]), and in [7] for instance, several conjugacy classes of Aut \\Gamma were studied, (where \\Gamma is the `random graph'). The purpose here is to attempt to describe as many conjugacy classes as possible in Aut Q, the group of homeomorphisms to itself of the set of rational numbers as a topological space. This very rich group has been studied in [1, 3, 4, 6, 9, 10, 11] for instance. Now in [4], this topological space was referred to as the `rational world'. Th