Theorems · Definition · manifolds

SmoothBumpCovering.toBumpCovering

{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} →
                        SmoothBumpCovering ι I M s → [T2Space M] → [IsManifold I (↑⊤) M] → BumpCovering ι M s

Reinterpret a SmoothBumpCovering as a continuous BumpCovering. Note that not every f : BumpCovering ι M s with smooth functions f i is a SmoothBumpCovering.

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

8 results in Mathlib

Foundations

Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensionalT2SpaceIsManifold