The Thom transversality theorem states that smooth maps transverse to a given submanifold form a dense subset of the space of all smooth maps in the appropriate smooth topology. More generally, the theorem applies to jet extensions transverse to a prescribed submanifold of a jet bundle.
Consequently, an arbitrary smooth map can be perturbed by an arbitrarily small amount to become transverse. If 
is transverse to a submanifold 
,
then 
is a submanifold of 
with codimension equal to that of 
in 
. This makes transversality a basic method for placing geometric
intersections in general position.
