stereoToFun_apply — Mathlib

English

The forward stereographic projection stereoToFun v is continuous on the set where innerSL v x ≠ 1.

Русский

Переходная стереографическая проекция stereoToFun v непрерывна на множестве where innerSL v x ≠ 1.

LaTeX

$$ContinuousOn\ Real (stereoToFun v)\ {x : E | innerSL _ v x \neq 1}$$

Lean4

@[simp]
theorem stereoToFun_apply (x : E) :
    stereoToFun v x = (2 / ((1 : ℝ) - innerSL ℝ v x)) • (ℝ ∙ v)ᗮ.orthogonalProjection x :=
  rfl

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