Theorems · Theorem · general topology
Path.source
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} (γ : Path x y), γ 0 = x- Defined in
- Mathlib.Topology.Path
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 119 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- unitIntervalstatement · cited by 607
- Pathstatement and proof · cited by 318
- Path.source'proof · cited by 1
Cited by27
Results whose statement or proof uses this declaration.
- JoinedIn.memproof · cited by 5
- Path.trans_symmproof · cited by 3
- Path.extend_zeroproof · cited by 3
- IsCoveringMap.map_liftPathQuotientproof · cited by 2
- Path.Homotopic.hpath_hextproof · cited by 2
- IsCoveringMap.monodromy_mapproof · cited by 2
- pathComponent_subset_componentproof · cited by 2
- Path.toHomotopyConstproof · cited by 2
- IsLocalHomeomorph.existsUnique_continuousMap_liftsproof · cited by 2
- Path.trans_continuous_familyproof · cited by 1
- IsCoveringMap.existsUnique_continuousMap_liftsproof · cited by 1
- JoinedIn.joined_subtypeproof · cited by 1