Theorems · Definition · general topology
TopologicalSpace.Opens.carrier
{α : Type u_2} → [inst : TopologicalSpace α] → TopologicalSpace.Opens α → Set αThe underlying set of a bundled TopologicalSpace.Opens object.
- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 167 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- TopologicalSpace.Opensstatement and proof · cited by 2,040
Cited by178
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.is_open'statement · cited by 139
- IsCompactOpenCoveredproof · cited by 18
- AlgebraicGeometry.StructureSheaf.comapstatement and proof · cited by 15
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invAppstatement and proof · cited by 8
- AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
- AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpensproof · cited by 6
- AlgebraicGeometry.StructureSheaf.comap_applystatement and proof · cited by 5
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_iSup_eq_topproof · cited by 5
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- IsCompactOpenCovered.iff_of_uniquestatement and proof · cited by 5
- AlgebraicGeometry.Scheme.Hom.preimage_iSupproof · cited by 4
- AlgebraicGeometry.IsOpenImmersion.isPullbackproof · cited by 4