Theorems · Definition · manifolds

SmoothPartitionOfUnity.toFun

{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 : optParam (Set M) Set.univ} →
                      SmoothPartitionOfUnity ι I M s → ι → ContMDiffMap I (modelWithCornersSelf ℝ ℝ) M ℝ ↑⊤

The family of functions forming the partition of unity.

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

4 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace