Theorems · Theorem · global analysis
SmoothBumpFunction.isClosed_image_of_isClosed
∀ {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] {s : Set M},
IsClosed s → s ⊆ Function.support ↑f → IsClosed (↑(extChartAt I c) '' s)- Defined in
- Mathlib.Geometry.Manifold.BumpFunction
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.imagestatement · cited by 5,609
- ModelWithCornersstatement and proof · cited by 2,462
- ChartedSpacestatement and proof · cited by 2,397
- FiniteDimensionalstatement and proof · cited by 1,854
- IsClosedstatement and proof · cited by 1,639
- PartialEquiv.toFunstatement · cited by 821
- Function.supportstatement and proof · cited by 610
Cited by1
Results whose statement or proof uses this declaration.
- SmoothBumpFunction.exists_r_pos_lt_subset_ballproof · cited by 1