Theorems · Definition · general topology
genericPoints.ofComponent
{α : Type u_1} → [inst : TopologicalSpace α] → [QuasiSober α] → ↑(irreducibleComponents α) → ↑(genericPoints α)The generic point of an irreducible component.
- Defined in
- Mathlib.Topology.Sober
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceQuasiSober
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Elemstatement and proof · cited by 7,166
- irreducibleComponentsstatement and proof · cited by 35
- QuasiSoberstatement and proof · cited by 31
- genericPointsstatement · cited by 10
- IsIrreducible.genericPointproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- genericPoints.component_ofComponentstatement · cited by 2
- genericPoints.equivproof · cited by 2
- genericPoints.isGenericPoint_ofComponentstatement · cited by 2
- genericPoints.closureproof · cited by 0
- genericPoints.component_surjectiveproof · cited by 0
- genericPoints.equiv_symm_applystatement · cited by 0
- genericPoints.ofComponent_componentstatement and proof · cited by 0