Theorems · Theorem · general topology
irreducibleComponent_mem_irreducibleComponents
∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X), irreducibleComponent x ∈ irreducibleComponents X- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 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.
Cites8
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
- Eq.leproof · cited by 605
- IsIrreducibleproof · cited by 59
- irreducibleComponentsstatement · cited by 35
- irreducibleComponentstatement and proof · cited by 10
- isIrreducible_irreducibleComponentproof · cited by 3
- eq_irreducibleComponentproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- isClosed_irreducibleComponentproof · cited by 1
- sUnion_irreducibleComponentsproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0
- genericPoints.closureproof · cited by 0