Motions in G-vector bundles (linear extensions) that are locally bounded and locally separated from zero

Abstract

One considers a G-vector bundle over a minimal G-space, possessing the property that the motion of each of its points is bounded and separated from zero over a sufficiently small neighborhood of any point of the base. It is proved that this bundle has the structure of a fiber space with a bicompact structure group and, moreover, the action of the group G preserves the projection onto a fiber of the fiber space. With the aid of this result, a series of theorems regarding the representations of bicompact groups are carried over to G-vector bundles or, in another terminology, to linear extensions of topological groups of transformations.