Theorems · Theorem · manifolds

SmoothBumpCovering.apply_ind

∀ {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) (x : M)
  (hx : x ∈ s), ↑(fs.toFun (fs.ind x hx)) x = 1

Defined in

Mathlib.Geometry.Manifold.PartitionOfUnity

Cited by

3 results in Mathlib

Foundations

Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensional