Theorems · Definition · general topology
genericPoints.equiv
{α : Type u_1} →
[inst : TopologicalSpace α] → [T0Space α] → [QuasiSober α] → ↑(genericPoints α) ≃ ↑(irreducibleComponents α)In a sober space, the generic points corresponds bijectively to irreducible components
- Defined in
- Mathlib.Topology.Sober
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- T0Spacestatement and proof · cited by 179
- irreducibleComponentsstatement · cited by 35
- QuasiSoberstatement and proof · cited by 31
- genericPointsstatement · cited by 10
- genericPoints.componentproof · cited by 7
- genericPoints.ofComponentproof · cited by 6
- genericPoints.component_ofComponentproof · cited by 2
- genericPoints.ofComponent_componentproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- genericPoints.equiv_applystatement and proof · cited by 0
- genericPoints.equiv_symm_applystatement and proof · cited by 0