Theorems · Theorem · algebraic topology

continuousOn_coordChange

∀ (R : Type u_1) {B : Type u_2} {F : Type u_3} {E : B → Type u_4} [inst : NontriviallyNormedField R]
  [inst_1 : (x : B) → AddCommMonoid (E x)] [inst_2 : (x : B) → Module R (E x)] [inst_3 : NormedAddCommGroup F]
  [inst_4 : NormedSpace R F] [inst_5 : TopologicalSpace B] [inst_6 : TopologicalSpace (Bundle.TotalSpace F E)]
  [inst_7 : (x : B) → TopologicalSpace (E x)] [inst_8 : FiberBundle F E] [inst_9 : VectorBundle R F E]
  (e e' : Bundle.Trivialization F Bundle.TotalSpace.proj) [inst_10 : MemTrivializationAtlas e]
  [inst_11 : MemTrivializationAtlas e'],
  ContinuousOn (fun b => ↑(Bundle.Trivialization.coordChangeL R e e' b)) (e.baseSet ∩ e'.baseSet)

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceFiberBundleVectorBundleMemTrivializationAtlasMemTrivializationAtlas