Theorems · Definition · general topology
IsPathConnected
{X : Type u_1} → [TopologicalSpace X] → Set X → PropA set F is path connected if it contains a point that can be joined to all other in F.
- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 120 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.
Cites3
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
- JoinedInproof · cited by 40
Cited by67
Results whose statement or proof uses this declaration.
- IsPathConnected.joinedInstatement and proof · cited by 8
- Convex.isPathConnectedstatement and proof · cited by 8
- IsPathConnected.isConnectedstatement and proof · cited by 7
- pathConnectedSpace_iff_univstatement · cited by 7
- isPathConnected_pathComponentInstatement · cited by 6
- IsOpen.pathComponentInproof · cited by 5
- LocallyPathConnectedSpace.path_connected_basisstatement · cited by 5
- IsPathConnected.imagestatement and proof · cited by 5
- Topology.IsInducing.isPathConnected_iffstatement · cited by 4
- isPathConnected_iff_pathConnectedSpacestatement and proof · cited by 4
- locallyPathConnectedSpace_iff_isOpen_pathComponentInproof · cited by 3
- IsPathConnected.image'statement and proof · cited by 3