Theorems · Theorem · global analysis
Diffeology.dSmooth_iff_contDiff
∀ {X : Type u_1} [inst : DiffeologicalSpace X] {Y : Type u_2} [inst_1 : NormedAddCommGroup X] [inst_2 : NormedSpace ℝ X]
[Diffeology.IsContDiffCompatible X] [inst_4 : NormedAddCommGroup Y] [inst_5 : NormedSpace ℝ Y]
[inst_6 : DiffeologicalSpace Y] [Diffeology.IsContDiffCompatible Y] [FiniteDimensional ℝ X] {f : X → Y},
Diffeology.DSmooth f ↔ ContDiff ℝ (↑⊤) f- Defined in
- Mathlib.Geometry.Diffeology.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement · cited by 9,680
- ENatstatement · cited by 4,985
- FiniteDimensionalstatement and proof · cited by 1,854
- WithTop.somestatement · cited by 1,128
- ContDiffstatement · cited by 352
- DiffeologicalSpacestatement and proof · cited by 60
- Diffeology.DSmoothstatement · cited by 16
- Diffeology.IsContDiffCompatiblestatement and proof · cited by 8
- ContDiff.dSmoothproof · cited by 1
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