Uniform Equiontinuity of Proper Group Actions
by
Sergey Antonyan
National Autonomous Iniversity of Mexico

Let G be a locally compact Hausdorff group. The notion of a proper G-action introduced by R. Palais in 1960 is a natural generalization of the classical notion of a dispersive dynamical system. We prove that for each proper G-action on a metrizable phase space X there is a uniformity U on X compatible with its topology such that the given action of G on X is U-uniformly equicontinuous. The Hájek's Problem on paracompactness of the orbit space of a dispersive dynamical system will be discussed.

Date received: February 3, 1998