Theorems · Theorem · general topology
PreirreducibleSpace.isPreirreducible_univ
∀ {X : Type u_3} {inst : TopologicalSpace X} [self : PreirreducibleSpace X], IsPreirreducible Set.univIn a preirreducible space, Set.univ is a preirreducible set.
- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PreirreducibleSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.univstatement · cited by 3,945
- IsPreirreduciblestatement · cited by 43
- PreirreducibleSpacestatement and proof · cited by 33
Cited by7
Results whose statement or proof uses this declaration.
- IrreducibleSpace.isIrreducible_univproof · cited by 7
- IsPreirreducible.of_subtypeproof · cited by 3
- nonempty_preirreducible_interproof · cited by 3
- Topology.IsOpenEmbedding.preirreducibleSpaceproof · cited by 1
- AlgebraicGeometry.genericPoint_eq_of_isOpenImmersionproof · cited by 1
- Function.Surjective.preirreducibleSpaceproof · cited by 0
- not_preirreducible_nontrivial_t2proof · cited by 0