Wir verwenden Cookies und Analyse-Tools, um die Nutzerfreundlichkeit der Internet-Seite zu verbessern und für Marketingzwecke. Wenn Sie fortfahren, diese Seite zu verwenden, nehmen wir an, dass Sie damit einverstanden sind. Zur Datenschutzerklärung.
Immersion (Mathematics)
CHF 43.15
Auf Lager
SKU
M50ST45MGKT
1 Verfügbar 
Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
Details
In mathematics, an immersion is a differentiable map between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M N is an immersion if Dpf : Tp 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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130234638
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T5mm
- Jahr 2009
- EAN 9786130234638
- Format Fachbuch
- ISBN 978-613-0-23463-8
- Titel Immersion (Mathematics)
- Untertitel Winding number, Homotopy principle, Mathematics, Smooth function, Differentiable manifold, Pushforward (differential), Injective function, Tangent space, Embedding, Diffeomorphism
- Gewicht 130g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
Bewertungen
Schreiben Sie eine Bewertung
