Theorems · Theorem · global analysis
Diffeology.isOpen_iff_preimages_plots
∀ {X : Type u_1} [inst : DiffeologicalSpace X] {u : Set X},
IsOpen u ↔ ∀ (n : ℕ) (p : EuclideanSpace ℝ (Fin n) → X), Diffeology.IsPlot p → IsOpen (p ⁻¹' u)- Defined in
- Mathlib.Geometry.Diffeology.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 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.
Cites10
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 · cited by 25,697
- ENNRealstatement · cited by 9,879
- Set.preimagestatement · cited by 4,946
- IsOpenstatement · cited by 2,400
- EuclideanSpacestatement · cited by 307
- DiffeologicalSpacestatement and proof · cited by 60
- Diffeology.IsPlotstatement · cited by 29
- Diffeology.dTopologystatement · cited by 5
- DiffeologicalSpace.isOpen_iff_preimages_plotsproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Diffeology.DSmooth.continuousproof · cited by 1
- Diffeology.IsPlot.continuousproof · cited by 0