R-isomorphisms of Transformation Groups and Prolongations

Abstract

In [8] the notion of a reparameterizing isomorphism of transformation groups, henceforth called an R-isomorphism, is introduced generalizing Ura's type-2 isomorphism (see [13]). We have shown [8] that an R-isomorphism is weaker than a transformation group isomorphism. For example, although R-isomorphisms preserve pointwise almost periodicity and minimality they do not preserve the existence of slices [7] or almost periodicity. This suggests that R-isomorphisms might be a useful classification tool in topological dynamics.