Theorems · Inductive type · general topology
TopologicalSpace.Opens
(α : Type u_2) → [TopologicalSpace α] → Type u_2
The type of open subsets of a topological space.
- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 2,040 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by2,565
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opensproof · cited by 1,149
- TopologicalSpace.Opens.mapstatement · cited by 645
- TopCat.Presheafproof · cited by 371
- TopCat.Presheaf.germstatement and proof · cited by 208
- Opens.grothendieckTopologystatement and proof · cited by 206
- AlgebraicGeometry.Scheme.Hom.appstatement · cited by 176
- TopCat.Presheaf.pushforwardproof · cited by 174
- TopologicalSpace.Opens.carrierstatement and proof · cited by 167
- PrimeSpectrum.basicOpenstatement · cited by 163
- AlgebraicGeometry.Scheme.basicOpenstatement · cited by 141
- TopologicalSpace.Opens.is_open'statement and proof · cited by 139
- AlgebraicGeometry.Scheme.Hom.appLEstatement · cited by 138
Showing the 200 most cited of 2,565.