Theorems · Theorem · general topology
IsIrreducible.nonempty
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsIrreducible s → s.Nonempty- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Nonemptystatement · cited by 2,627
- IsIrreduciblestatement and proof · cited by 59
Cited by7
Results whose statement or proof uses this declaration.
- IsIrreducible.imageproof · cited by 7
- IsIrreducible.isConnectedproof · cited by 2
- topologicalKrullDim_zero_of_discreteTopologyproof · cited by 2
- Subtype.irreducibleSpaceproof · cited by 1
- isIrreducible_iff_sInterproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isIrreducible_preimageproof · cited by 1