Theorems · Theorem · manifolds

SmoothPartitionOfUnity.IsSubordinate.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 : SmoothPartitionOfUnity ι I M s} {U : ι → Set M},
  f.IsSubordinate U → f.toPartitionOfUnity.IsSubordinate U

Alias of the reverse direction of SmoothPartitionOfUnity.isSubordinate_toPartitionOfUnity.

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

0 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace