Theorems · Theorem · general topology
isIrreducible_irreducibleComponent
∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X}, IsIrreducible (irreducibleComponent x)- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.
Cites5
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
- IsIrreduciblestatement · cited by 59
- irreducibleComponentstatement · cited by 10
- mem_irreducibleComponentproof · cited by 6
- irreducibleComponent_propertyproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- irreducibleComponent_mem_irreducibleComponentsproof · cited by 5
- irreducibleComponent_subset_connectedComponentproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0