toEuclidean — Mathlib

English

If r > 0, then the center x belongs to the open ball of radius r around itself.

Русский

Если r > 0, то x принадлежит открытой сфере радиуса r вокруг x.

LaTeX

$$hr > 0 ⇒ x ∈ ball x r$$

Lean4

/-- If `E` is a finite-dimensional space over `ℝ`, then `toEuclidean` is a continuous `ℝ`-linear
equivalence between `E` and the Euclidean space of the same dimension. -/
def toEuclidean : E ≃L[ℝ] EuclideanSpace ℝ (Fin <| finrank ℝ E) :=
  ContinuousLinearEquiv.ofFinrankEq finrank_euclideanSpace_fin.symm

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