toOpenPartialHomeomorph — Mathlib

English

The coe of the open partial homeomorph equals the function f for ContDiffAt settings.

Русский

Коэффициент открытого частичного гомоморфа совпадает с функцией f в рамках ContDiffAt.

LaTeX

$$$(hf.toOpenPartialHomeomorph f hf' hn : E \to F) = f$$$

Lean4

/-- Given a `ContDiff` function over `𝕂` (which is `ℝ` or `ℂ`) with an invertible
derivative at `a`, returns an `OpenPartialHomeomorph` with `to_fun = f` and `a ∈ source`. -/
def toOpenPartialHomeomorph (hf : ContDiffAt 𝕂 n f a) (hf' : HasFDerivAt f (f' : E →L[𝕂] F) a) (hn : 1 ≤ n) :
    OpenPartialHomeomorph E F :=
  (hf.hasStrictFDerivAt' hf' hn).toOpenPartialHomeomorph f

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