Theorems · Definition · general topology
irreducibleSetEquivPoints
{α : Type u_1} →
[inst : TopologicalSpace α] → [QuasiSober α] → [inst_2 : T0Space α] → TopologicalSpace.IrreducibleCloseds α ≃o αThe closed irreducible subsets of a sober space bijects with the points of the space.
- Defined in
- Mathlib.Topology.Sober
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- closureproof · cited by 1,254
- OrderIsostatement · cited by 874
- T0Spacestatement and proof · cited by 179
- QuasiSoberstatement and proof · cited by 31
- TopologicalSpace.IrreducibleClosedsstatement and proof · cited by 30
- IsIrreducible.genericPointproof · cited by 8
- specializationOrderstatement · cited by 3
- TopologicalSpace.IrreducibleCloseds.isIrreducible'proof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.coheight_eqproof · cited by 1
- PrimeSpectrum.pointsEquivIrreducibleClosedsproof · cited by 1
- coe_irreducibleEquivPoints_symm_applystatement · cited by 0
- PrimeSpectrum.zeroLocusEquivIrreducibleClosedsproof · cited by 0
- irreducibleSetEquivPoints.congr_simpstatement and proof · cited by 0