of_discreteTopology — Mathlib

English

The discrete space M carries a C^n-manifold structure modeled on the trivial model I = modelWithCornersSelf 𝕜 E, provided there is a unique E.

Русский

Для дискретного пространства M существует C^n-многообразие, моделируемое тривиальной моделью I = modelWithCornersSelf 𝕜 E, при условии уникальности E.

LaTeX

$$DiscreteTopology(M) ∧ Unique(E) ⇒ IsManifold(modelWithCornersSelf 𝕜 E, n, M)$$

Lean4

/-- A discrete space `M` is a smooth manifold over the trivial model on a trivial normed space. -/
theorem of_discreteTopology [DiscreteTopology M] [Unique E] : IsManifold (modelWithCornersSelf 𝕜 E) n M := by
  apply isManifold_of_contDiffOn _ _ _ (fun _ _ _ _ ↦ contDiff_of_subsingleton.contDiffOn)

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