ABSTRACT
Let (X, T] be a topological space and let H(X) denote the collection of all self-homeomorph-isms on X. We say that X is homogeneous provided that for each pair of points x,y 6 X there is some homeomorphism h e H(X) such that h(x] = y. For x € X define Ex : ( H ( X ) , T * ) -»• (X,T) to be the evaluation map, Ex(ti) = h(x), where T* is some topology on H(X).
