A Characterization of Orbits
James W. England · Proceedings of the American Mathematical Society · 1966
In this paper we give a necessary and sufficient condition in order that the orbit of a point be a homeomorphic image of the phase group in a transformation group.The general reference for definitions is [2], Throughout this paper iX, T, ir) will denote a transformation group for which X is a first countable Hausdorff space.The phase group P will be assumed to be generative, that is, T is isomorphic to CXPmX7"where Cis acompact abelian group, R is the additive group of real numbers, 7 is the additive group of integers, and m and ra are non-negative integers [4].P will denote a replete semigroup in P which is distinct from P. Let