Theorems · Theorem · global analysis

ContinuousLinearEquiv.contMDiffWithinAt_transContinuousLinearEquiv_left

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {F : Type u_4}
  [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜 F] {H : Type u_5} [inst_7 : TopologicalSpace H]
  {H' : Type u_6} [inst_8 : TopologicalSpace H'] {I : ModelWithCorners 𝕜 E H} {I' : ModelWithCorners 𝕜 E' H'}
  {M : Type u_9} [inst_9 : TopologicalSpace M] [inst_10 : ChartedSpace H M] {M' : Type u_10}
  [inst_11 : TopologicalSpace M'] [inst_12 : ChartedSpace H' M'] {n : WithTop ℕ∞} (e : E ≃L[𝕜] F) {f : M → M'} {x : M}
  {s : Set M}, ContMDiffWithinAt (I.transContinuousLinearEquiv e) I' n f s x ↔ ContMDiffWithinAt I I' n f s x

Defined in

Mathlib.Geometry.Manifold.Diffeomorph

Cited by

0 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace