Theorems · Theorem · manifolds

BumpCovering.contMDiff_toPartitionOfUnity

∀ {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 : BumpCovering ι M s),
  (∀ (i : ι), ContMDiff I (modelWithCornersSelf ℝ ℝ) ↑⊤ ⇑(f i)) →
    ∀ (i : ι), ContMDiff I (modelWithCornersSelf ℝ ℝ) ↑⊤ ⇑(f.toPartitionOfUnity i)

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

0 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace