Theorems · Definition · general topology
pathSetoid
(X : Type u_1) → [TopologicalSpace X] → Setoid X
The setoid corresponding the equivalence relation of being joined by a continuous path.
- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 127 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Joinedproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- ZerothHomotopyproof · cited by 15
- ZerothHomotopy.mkproof · cited by 11
- pathConnectedSpace_iff_zerothHomotopyproof · cited by 0
- connectedComponentSetoid_eq_pathSetoidstatement · cited by 0