Theorems · Theorem · global analysis

SmoothBumpFunction.contMDiff

∀ {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) [inst_5 : FiniteDimensional ℝ E] [T2Space M] [IsManifold I (↑⊤) M],
  ContMDiff I (modelWithCornersSelf ℝ ℝ) ↑⊤ ↑f

A smooth bump function is infinitely smooth.

Defined in

Mathlib.Geometry.Manifold.BumpFunction

Cited by

2 results in Mathlib

Foundations

Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceFiniteDimensionalT2SpaceIsManifold