Theorems · Definition · global analysis

stereographic

{E : Type u_1} →
  [inst : NormedAddCommGroup E] →
    [inst_1 : InnerProductSpace ℝ E] → {v : E} → ‖v‖ = 1 → OpenPartialHomeomorph ↑(Metric.sphere 0 1) ↥(ℝ ∙ v)ᗮ

Stereographic projection from the unit sphere in E, centred at a unit vector v in E; this is the version as an open partial homeomorphism.

Defined in

Mathlib.Geometry.Manifold.Instances.Sphere

Cited by

10 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpace