hasGroupoid_continuousGroupoid — Mathlib

English

Any charted-space structure is compatible with the groupoid of all open partial homeomorphisms.

Русский

Любая структура чартизованного пространства совместима с группоидом всех открытых частичных гомоморфизмов.

LaTeX

$$$HasGroupoid\ M\ (\text{continuousGroupoid } H)$, with compatibility for all atlas charts.$$

Lean4

/-- Any charted space structure is compatible with the groupoid of all open partial
homeomorphisms. -/
instance hasGroupoid_continuousGroupoid : HasGroupoid M (continuousGroupoid H) :=
  by
  refine ⟨fun _ _ ↦ ?_⟩
  rw [continuousGroupoid, mem_groupoid_of_pregroupoid]
  simp only [and_self_iff]

Похожие утверждения