Theorems · Theorem · algebraic topology

FiberBundle.chartedSpace_chartAt_symm_fst

∀ {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),
  ∀ y ∈ (chartAt (ModelProd HB F) x).target, (↑(chartAt (ModelProd HB F) x).symm y).proj = ↑(chartAt HB x.proj).symm y.1

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiberBundle