Group actions on one-manifolds, II: Extensions of Hölder's Theorem

This self-contained paper is part of a series seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. In this paper we consider groups which act on with restrictions on the fixed point set of each element. One result is a topological characterization of affine groups in as those groups whose elements have at most one fixed point.