In mathematics, a subbundle of a vector bundle on a topological space is a collection of linear subspaces of the fibers of at in that make up a vector bundle in their own right. In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors). If a set of vector fields span the vector space and all Lie commutators are linear combinations of the then one says that is an involutive distribution. See also Fiber bundles