Subbundle

In mathematics, a subbundle "U" of a vector bundle "V" on a topological space "X" is a collection of linear subspaces "U""x" of the fibers "V""x" of "V" at "x" in "X", 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 "Y"k span the vector space "U", and all Lie commutators ["Y"i,"Y"j] are linear combinations of the "Y"k, then one says that "U" is an involutive distribution.