Theorems · Theorem · algebraic topology

ContMDiffVectorBundle.of_le

∀ {𝕜 : Type u_1} {B : Type u_2} {F : Type u_4} {E : B → Type u_6} [inst : NontriviallyNormedField 𝕜] {EB : Type u_7}
  [inst_1 : NormedAddCommGroup EB] [inst_2 : NormedSpace 𝕜 EB] {HB : Type u_8} [inst_3 : TopologicalSpace HB]
  {IB : ModelWithCorners 𝕜 EB HB} [inst_4 : TopologicalSpace B] [inst_5 : ChartedSpace HB B]
  [inst_6 : (x : B) → AddCommMonoid (E x)] [inst_7 : (x : B) → Module 𝕜 (E x)] [inst_8 : NormedAddCommGroup F]
  [inst_9 : NormedSpace 𝕜 F] [inst_10 : TopologicalSpace (Bundle.TotalSpace F E)]
  [inst_11 : (x : B) → TopologicalSpace (E x)] [inst_12 : FiberBundle F E] [inst_13 : VectorBundle 𝕜 F E]
  {m n : WithTop ℕ∞}, m ≤ n → ∀ [h : ContMDiffVectorBundle n F E IB], ContMDiffVectorBundle m F E IB

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceFiberBundleVectorBundleContMDiffVectorBundle