Theorems · Theorem · algebraic topology

FiberBundle.chartedSpace_chartAt

∀ {B : Type u_2} {F : Type u_4} {E : B → Type u_6} [inst : TopologicalSpace F]
  [inst_1 : TopologicalSpace (Bundle.TotalSpace F E)] [inst_2 : (x : B) → TopologicalSpace (E x)] {HB : Type u_7}
  [inst_3 : TopologicalSpace HB] [inst_4 : TopologicalSpace B] [inst_5 : ChartedSpace HB B] [inst_6 : FiberBundle F E]
  (x : Bundle.TotalSpace F E),
  chartAt (ModelProd HB F) x =
    (trivializationAt F E x.proj).trans ((chartAt HB x.proj).prod (OpenPartialHomeomorph.refl F))

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

6 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiberBundle