Theorems · Theorem · general topology
Path.continuous
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} (γ : Path x y), Continuous ⇑γ- Defined in
- Mathlib.Topology.Path
- Cited by
- 3 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Continuousstatement · cited by 2,592
- unitIntervalstatement · cited by 607
- Pathstatement and proof · cited by 318
- ContinuousMap.continuous_toFunproof · cited by 47
- Path.toContinuousMapproof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- Path.castproof · cited by 22
- pathComponent_subset_componentproof · cited by 2
- Path.continuous_extendproof · cited by 1
- Circle.not_isPreconnected_compl_pairproof · cited by 0