Theorems · Theorem · manifolds

SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq

∀ {ι : Type uι} {E : Type uE} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type uH}
  [inst_2 : TopologicalSpace H] {I : ModelWithCorners ℝ E H} {M : Type uM} [inst_3 : TopologicalSpace M]
  [inst_4 : ChartedSpace H M] [inst_5 : FiniteDimensional ℝ E] {s : Set M} (fs : SmoothBumpCovering ι I M s)
  [inst_6 : T2Space M] [inst_7 : IsManifold I (↑⊤) M] (i : ι) (x : M),
  ∃ t, ⇑(fs.toSmoothPartitionOfUnity i) =ᶠ[nhds x] ↑(fs.toFun i) * ∏ j ∈ t with WellOrderingRel j i, (1 - ↑(fs.toFun j))

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

0 results in Mathlib

Foundations

Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensionalT2SpaceIsManifold