Theorems · Theorem · general topology
IsPreirreducible.open_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] {t U : Set X}, IsPreirreducible t → IsOpen U → U ⊆ t → IsPreirreducible U- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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
- Set.Nonemptyproof · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- Set.eq_empty_or_nonemptyproof · cited by 248
- IsPreirreduciblestatement and proof · cited by 43
- isPreirreducible_emptyproof · cited by 3
- IsPreirreducible.subset_irreducibleproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsPreirreducible.of_subset_iUnionproof · cited by 1
- IsPreirreducible.interiorproof · cited by 0