English
The source of the local inverse is open in the topology.
Русский
Область определения локального обратного открыта в топологии.
LaTeX
$$IsOpen hf.localInverse.source$$
Lean4
protected theorem mdifferentiableAt (hn : 1 ≤ n) {x : M} (hx : x ∈ Φ.source) : MDifferentiableAt I J Φ x :=
(Φ.mdifferentiableOn hn x hx).mdifferentiableAt
(Φ.open_source.mem_nhds hx)
/- We could add lots of additional API (following `Diffeomorph` and `OpenPartialHomeomorph`),
such as
* further continuity and differentiability lemmas
* refl and trans instances; lemmas between them.
As this declaration is meant for internal use only, we keep it simple. -/