Theorems · Theorem · algebraic topology

Bundle.ContinuousRiemannianMetric.mk.sizeOf_spec

∀ {B : Type u_4} [inst : TopologicalSpace B] {F : Type u_5} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ F]
  {E : B → Type u_6} [inst_3 : TopologicalSpace (Bundle.TotalSpace F E)] [inst_4 : (b : B) → TopologicalSpace (E b)]
  [inst_5 : (b : B) → AddCommGroup (E b)] [inst_6 : (b : B) → Module ℝ (E b)] [inst_7 : FiberBundle F E]
  [inst_8 : VectorBundle ℝ F E] [inst_9 : SizeOf B] [inst_10 : SizeOf F] [inst_11 : (a : B) → SizeOf (E a)]
  (inner : (b : B) → E b →L[ℝ] E b →L[ℝ] ℝ) (symm : ∀ (b : B) (v w : E b), ((inner b) v) w = ((inner b) w) v)
  (pos : ∀ (b : B) (v : E b), v ≠ 0 → 0 < ((inner b) v) v)
  (isVonNBounded : ∀ (b : B), Bornology.IsVonNBounded ℝ {v | ((inner b) v) v < 1})
  (continuous : Continuous fun b => ⟨b, inner b⟩),
  sizeOf { inner := inner, symm := symm, pos := pos, isVonNBounded := isVonNBounded, continuous := continuous } =
    1 + sizeOf continuous

Defined in

Mathlib.Topology.VectorBundle.Riemannian

Cited by

0 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceAddCommGroupModuleFiberBundleVectorBundleSizeOfSizeOfSizeOf