Expansive self-homeomorphisms on G-spaces

Beginning with examples, the notion ofG-expansiveness over a metric spaceX on which a topological groupG acts is introduced. Some conditions are determined under which expansiveness onX impliesG-expansiveness. A characterization of aG-expansive homeomorphism is obtained which in turn gives a sufficient condition for the homeomorphic extension of aG-expansive homeomorphism to beG-expansive. At the end, some results are stated in the form of concluding remarks.