Theorems · Theorem · general topology
IsPreconnected.subsingleton
∀ {α : Type u} [inst : TopologicalSpace α] [TotallyDisconnectedSpace α] {s : Set α}, IsPreconnected s → s.Subsingleton- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- TotallyDisconnectedSpacestatement and proof · cited by 295
- Set.Subsingletonstatement · cited by 276
- Set.subset_univproof · cited by 228
- IsPreconnectedstatement and proof · cited by 205
- TotallyDisconnectedSpace.isTotallyDisconnected_univproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Real.Angle.sign_eq_of_continuousOnproof · cited by 3
- subsingleton_of_preconnected_totallyDisconnectedproof · cited by 1
- IsPreconnected.constantproof · cited by 1
- Continuous.image_connectedComponent_eq_singletonproof · cited by 1
- TotallyDisconnectedSpace.eq_of_continuousproof · cited by 0