Theorems · Theorem · general topology
irreducibleComponent_property
∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X),
IsPreirreducible (irreducibleComponent x) ∧
{x} ⊆ irreducibleComponent x ∧
∀ (u : Set X), IsPreirreducible u → irreducibleComponent x ⊆ u → u = irreducibleComponent x- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 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.
Cites6
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
- IsPreirreduciblestatement · cited by 43
- irreducibleComponentstatement · cited by 10
- exists_preirreducibleproof · cited by 2
- isPreirreducible_singletonproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- mem_irreducibleComponentproof · cited by 6
- isIrreducible_irreducibleComponentproof · cited by 3
- eq_irreducibleComponentproof · cited by 1