Theorems · Theorem · general topology
irreducibleComponents_eq_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X] [IrreducibleSpace X], irreducibleComponents X = {Set.univ}- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.univstatement · cited by 3,945
- Set.extproof · cited by 2,266
- Set.subset_univproof · cited by 228
- IsIrreducibleproof · cited by 59
- IrreducibleSpacestatement and proof · cited by 40
- irreducibleComponentsstatement · cited by 35
- IrreducibleSpace.isIrreducible_univproof · cited by 7
- IsGreatest.maximal_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.irreducibleComponentOpen_eq_topproof · cited by 0
- genericPoints_eq_singletonproof · cited by 0