Continuous liftings of vector fields (Q5937146)

We improve the known theorems on the continuous lifting of vector fields defined on a stratum \(X\) of a regular stratification of a closed set of a smooth manifold by introducing the notion of canonical distribution \({\mathcal D}_X\): a continuous \(l\)-bundle near \(X\) \((l=\dim X)\) such that the lifting on \({\mathcal D}_X\) of each vector field defined on \(X\) gives a canonical continuous stratified extension.