Theorems · Inductive type · general topology
LocallyPathConnectedSpace
(X : Type u_4) → [TopologicalSpace X] → Prop
A topological space is locally path connected if, at every point, path connected neighborhoods form a neighborhood basis.
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by59
Results whose statement or proof uses this declaration.
- IsOpen.pathComponentInstatement and proof · cited by 5
- LocallyPathConnectedSpace.path_connected_basisstatement and proof · cited by 5
- connectedComponentsEquivZerothHomotopystatement and proof · cited by 3
- locallyPathConnectedSpace_iff_isOpen_pathComponentInstatement and proof · cited by 3
- IsOpen.locallyPathConnectedSpacestatement and proof · cited by 3
- IsOpen.pathComponentstatement and proof · cited by 2
- Topology.IsQuotientMap.locallyPathConnectedSpacestatement and proof · cited by 2
- IsClopen.pathComponentstatement and proof · cited by 2
- LocallyPathConnectedSpace.coinducedstatement and proof · cited by 2
- LocallyPathConnectedSpace.of_basesstatement · cited by 2
- IsLocalHomeomorph.existsUnique_continuousMap_liftsstatement and proof · cited by 2
- PathConnectedSpace.of_locallyPathConnectedSpacestatement and proof · cited by 2