Theorems · Definition · general topology
irreducibleComponent
{X : Type u_1} → [TopologicalSpace X] → X → Set XA maximal irreducible set that contains a given point.
- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
Cited by10
Results whose statement or proof uses this declaration.
- mem_irreducibleComponentstatement · cited by 6
- irreducibleComponent_mem_irreducibleComponentsstatement and proof · cited by 5
- irreducibleComponent_propertystatement · cited by 3
- isIrreducible_irreducibleComponentstatement · cited by 3
- eq_irreducibleComponentstatement · cited by 1
- isClosed_irreducibleComponentstatement and proof · cited by 1
- irreducibleComponent_subset_connectedComponentstatement · cited by 0
- genericPoints.closureproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0