Theorems · Definition · general topology
irreducibleComponents
(X : Type u_3) → [TopologicalSpace X] → Set (Set X)
The set of irreducible components of a topological space.
- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Maximalproof · cited by 211
- IsIrreducibleproof · cited by 59
Cited by47
Results whose statement or proof uses this declaration.
- genericPointsproof · cited by 10
- isClosed_of_mem_irreducibleComponentsstatement and proof · cited by 9
- genericPoints.componentstatement · cited by 7
- genericPoints.ofComponentstatement and proof · cited by 6
- irreducibleComponent_mem_irreducibleComponentsstatement · cited by 5
- TopologicalSpace.NoetherianSpace.finite_irreducibleComponentsstatement and proof · cited by 3
- PrimeSpectrum.vanishingIdeal_irreducibleComponentsstatement · cited by 2
- PrimeSpectrum.vanishingIdeal_mem_minimalPrimesstatement and proof · cited by 2
- genericPoints.component_injectivestatement · cited by 2
- genericPoints.component_ofComponentstatement and proof · cited by 2
- genericPoints.equivstatement · cited by 2
- genericPoints.isGenericPoint_ofComponentstatement and proof · cited by 2