Theorems · Theorem · manifolds

SmoothBumpCovering.IsSubordinate.support_subset

∀ {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} {fs : SmoothBumpCovering ι I M s}
  {U : M → Set M}, fs.IsSubordinate U → ∀ (i : ι), Function.support ↑(fs.toFun i) ⊆ U (fs.c i)

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

1 results in Mathlib

Foundations

Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensional