| In this dissertation we investigate the Homeomorphism group of the interval Hom([0, 1]), the structure of certain closed subgroups, and the equivalence relations induced by its actions. We compare this group to the better understood S∞, the group of permutations of the natural numbers.; Chapter two looks at the free actions of Hom([0, 1]) on [0, 1] and of Hom([0, 1]2) on [0, 1] 2. Chapter three investigates universal actions of Hom([0, 1]), extending a result of Gao. The final chapter looks at some open problems concerning Hom([0, 1]). |
