Theorems · Theorem · algebraic topology

Bundle.Trivialization.continuousLinearMapAt_apply_of_mem

∀ (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]
  (e : Bundle.Trivialization F Bundle.TotalSpace.proj) [inst_9 : Bundle.Trivialization.IsLinear R e] {b : B},
  b ∈ e.baseSet → ∀ (y : E b), (Bundle.Trivialization.continuousLinearMapAt R e b) y = (↑e ⟨b, y⟩).2

Defined in

Mathlib.Topology.VectorBundle.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceFiberBundleBundle.Trivialization.IsLinear