Theorems · Definition · manifolds

SmoothPartitionOfUnity.IsSubordinate

{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} → SmoothPartitionOfUnity ι I M s → (ι → Set M) → Prop

A smooth partition of unity f i is subordinate to a family of sets U i indexed by the same type if for each i the closure of the support of f i is a subset of U i.

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

10 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace