Equivariant semialgebraic vector bundles (Q697622)

The authors prove that every semialgebraic \(G\)-vector bundle over a semialgebraic \(G\)-set \(E\) has a semialgebraic classifying \(G\)-map and moreover that the set of semialgebraic \(G\)-isomorphism classes of semialgebraic \(G\)-vector bundles over \(E\) corresponds bijectively to the set of topological \(G\)-isomorphism classes of topological \(G\)-vector bundles over \(E\). An interesting application of these theorems is the equivariant semialgebraic version of the homotopy property for semialgebraic \(G\)-vector bundles proven in the final part of the paper.