A local diffeomorphism is a smooth map between manifolds that, for every point in its domain, restricts to a diffeomorphism from some open neighborhood of that point onto an open subset of the target manifold. The inverse function theorem gives a working criterion: a smooth map is a local diffeomorphism exactly where its derivative is a linear isomorphism between the corresponding tangent spaces, which in particular forces the two manifolds to have the same dimension. Local diffeomorphisms are therefore exactly the smooth maps whose derivative is everywhere invertible. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Connections
In Branch
Source Local Diffeomorphism (Wikipedia)
Is Kind Of Object
Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.
Sources
1. Local Diffeomorphism (Wikipedia)
In Branch: Differential Topology, Lead sentenceQuote, In Branch: Differential Topology, Lead sentence
In mathematics, more specifically differential topology, a local diffeomorphism is intuitively a map between smooth manifolds that
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.