Theorems · Theorem · algebraic geometry

ChartedSpace.restrictLocallyRingedSpaceIso_hom

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {EM : Type u_1} [inst_1 : NormedAddCommGroup EM]
  [inst_2 : NormedSpace 𝕜 EM] {HM : Type u_2} [inst_3 : TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
  {M : Type u} [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace HM M] (U : TopologicalSpace.Opens M),
  (ChartedSpace.restrictLocallyRingedSpaceIso U).hom =
    AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift (ChartedSpace.locallyRingedSpaceMap Subtype.val ⋯)
      ((ChartedSpace.locallyRingedSpace IM M).ofRestrict ⋯) ⋯

Defined in

Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace

Cited by

0 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace