Theorems · Definition · general topology
IsPreconnected
{α : Type u} → [TopologicalSpace α] → Set α → PropA preconnected set is one where there is no non-trivial open partition.
- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 205 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 27 definitions · 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.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
Cited by210
Results whose statement or proof uses this declaration.
- IsConnectedproof · cited by 116
- connectedComponentproof · cited by 68
- IsConnected.isPreconnectedstatement · cited by 36
- PreconnectedSpace.isPreconnected_univstatement · cited by 26
- IsPreconnected.imagestatement and proof · cited by 24
- IsTotallyDisconnectedproof · cited by 14
- Convex.isPreconnectedstatement · cited by 14
- isPreconnected_emptystatement · cited by 14
- isPreconnected_connectedComponentstatement and proof · cited by 12
- Topology.IsInducing.isPreconnected_imagestatement and proof · cited by 11
- IsPreconnected.subset_connectedComponentstatement and proof · cited by 10
- Set.OrdConnected.isPreconnectedstatement · cited by 9
Showing the 200 most cited of 210.