Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Immersion (Mathematics)

Immersion (Mathematics)

Miller, Frederic P.
Vandome, Agnes F.
McBrewster, John

Paperback

General Mathematics

Currently unavailable to order

ISBN10: 6130234635
ISBN13: 9786130234638
Publisher: Alphascript Pub
Pages: 78
Weight: 0.28
Height: 0.18 Width: 9.01 Depth: 5.98
Language: English
In mathematics, an immersion is a differentiable map between differentiable manifolds whose derivative is everywhere injective. Explicitly, f: M N is an immersion if D_pf: T_p M to T_{f(p)}N, is an injective map at every point p of M (where the notation TpX represents the tangent space of X at the point p). Equivalently, f is an immersion if it has constant rank equal to the dimension of M: operatorname{rank}, f = dim M. The map f itself need not be injective, only its derivative. A related concept is that of an embedding. A smooth embedding is an injective immersion f: M N which is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding - i.e. for any point xin M there is a neighbourhood, Usubset M, of x such that f: Uto N is an embedding, and conversely a local embedding is an immersion. An injectively immersed submanifold that is not an embedding. If M is compact, an injective immersion is an embedding, but if M is not compact then injective immersions need not be embeddings; compare to continuous bijections versus homeomorphisms.

Also in

General Mathematics

View All