Rectangular conditions in products and equivariant completions (Q409698)

The author gives a general condition that characterizes when an action extends to a completion of a phase space. He provides an example of a \(G\)-space that has no Dieudonné complete \(G\)-extension. He also gives different sufficient rectangular conditions in products for the action to extend to the Stone-Čech compactification, the Hewitt realcompactification and the Dieudonné completion of a space. Finally, boundedness, uniform equicontinuity and quasi-boundedness of actions are characterized by the uniform continuity of the action on the piecewise semi-uniform product.