An

-dimensional manifold

is a submanifold of another

-dimensional manifold

(

) if

a)

(

is a subset of

)

b) The inclusion map

with

is an embedding

(Which means that for each

the differential

is

and that the inclusion map

is a homomorphism)

So I only care for finite dimensional differential manifolds.

Well I obviously have (a). Could I use the Reverse function therem for the differential?