Theorems · Theorem · manifolds

SmoothPartitionOfUnity.sum_eq_one

∀ {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] {s : Set M} (f : SmoothPartitionOfUnity ι I M s) {x : M}, x ∈ s → ∑ᶠ (i : ι), (f i) x = 1

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

4 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace