Theorems · Theorem · algebraic topology

VectorPrebundle.mk_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 : (x : B) → TopologicalSpace (E x)]
  (a : VectorPrebundle R F E) {e e' : Bundle.Pretrivialization F Bundle.TotalSpace.proj}
  (he : e ∈ a.pretrivializationAtlas) (he' : e' ∈ a.pretrivializationAtlas) {b : B},
  b ∈ e.baseSet ∩ e'.baseSet → ∀ (v : F), (b, (a.coordChange he he' b) v) = ↑e' ⟨b, e.symm b v⟩

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace