Title: Regulous vector bundles,
Abstract: Among recently introduced new notions in real algebraic geometry is that of
regulous functions. Such functions form a foundation for the development of
regulous geometry. Several interesting results on regulous varieties and
regulous sheaves are already available. In this paper, we define and
investigate regulous vector bundles. We establish algebraic and geometric
properties of such vector bundles, and identify them with stratified-algebraic
vector bundles. Furthermore, using new results on curve-rational functions, we
characterize regulous vector bundles among families of vector spaces
parametrized by an affine regulous variety. We also study relationships between
regulous and topological vector bundles.