ON CERTAIN HOMEOMORPHISM GROUPS

et R, 2, J, and C denote respectively the reals, the rationals, the ir rationals and the Cantor set endowed with their usual topologies. For any topological space X let G(X) denote the group of homeomorphisms of X. Let H(R) denote the group of orientation preserving homeomorphisms of R, S(omega) the group of permutations of the set N of natural numb ers and G0(R(n)) the group of homeomorphisms of R(n) with compact supp ort for any integer n greater-than-or-equal-to 1. We show that G F c an be imbedded in G when G is any one of the groups G(2), G(J), G(C), H(R), S(omega) or G0(R(n)) where F is a free group of rank c = # R.