Theorems · Theorem · global analysis

SmoothBumpFunction.eventuallyEq_one_of_dist_lt

∀ {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] {c : M}
  (f : SmoothBumpFunction I c) {x : M} [inst_5 : FiniteDimensional ℝ E],
  x ∈ (chartAt H c).source → dist (↑(extChartAt I c) x) (↑(extChartAt I c) c) < f.rIn → ↑f =ᶠ[nhds x] 1

Defined in

Mathlib.Geometry.Manifold.BumpFunction

Cited by

2 results in Mathlib

Foundations

Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensional