sphere — Mathlib

English

The n-sphere is the set of points in ℝ^{n+1} with norm equal to 1, endowed with the subspace topology.

Русский

n‑сфера — множество точек в ℝ^{n+1} с нормой, равной 1, с вложенной топологией.

LaTeX

$$$S^n = \\{ x \\in \\mathbb{R}^{n+1} : \\|x\\| = 1 \\}. $$$

Lean4

/-- The `n`-sphere is the set of points in ℝⁿ⁺¹ whose norm equals `1`,
endowed with the subspace topology. -/
noncomputable def sphere (n : ℕ) : TopCat.{u} :=
  diskBoundary (n + 1)

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