Theorems · Definition · global analysis
DiffeologicalSpace.plots
{X : Type u_1} → [self : DiffeologicalSpace X] → (n : ℕ) → Set (EuclideanSpace ℝ (Fin n) → X)The plots EuclideanSpace ℝ (Fin n) → X representing the smooth ways to map
EuclideanSpace ℝ (Fin n) into X. This is the main
piece of data underlying the diffeology.
- Defined in
- Mathlib.Geometry.Diffeology.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DiffeologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- EuclideanSpacestatement · cited by 307
- DiffeologicalSpacestatement and proof · cited by 60
Cited by7
Results whose statement or proof uses this declaration.
- Diffeology.IsPlotproof · cited by 29
- DiffeologicalSpace.plot_reparamstatement · cited by 1
- DiffeologicalSpace.replaceDTopologyproof · cited by 1
- DiffeologicalSpace.le_iffstatement and proof · cited by 1
- DiffeologicalSpace.constant_plotsstatement · cited by 1
- DiffeologicalSpace.isOpen_iff_preimages_plotsstatement · cited by 1
- DiffeologicalSpace.localitystatement · cited by 0