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Anglický jazyk
Immersion (Mathematics)
Autor: Frederic P. Miller
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... Viac o knihe
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O knihe
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.
- Vydavateľstvo: OmniScriptum
- Rok vydania: 2026
- Formát: Paperback
- Rozmer: 220 x 150 mm
- Jazyk: Anglický jazyk
- ISBN: 9786130234638
