Theorems · Definition · general topology
Path.pi
{ι : Type u_3} →
{χ : ι → Type u_4} →
[inst : (i : ι) → TopologicalSpace (χ i)] → {as bs : (i : ι) → χ i} → ((i : ι) → Path (as i) (bs i)) → Path as bsGiven a family of paths, one in each Xᵢ, we take their pointwise product to get a path in Π i, Xᵢ.
- Defined in
- Mathlib.Topology.Path
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 121 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- ContinuousMapproof · cited by 2,491
- unitIntervalproof · cited by 607
- Pathstatement and proof · cited by 318
- Path.toContinuousMapproof · cited by 27
- ContinuousMap.piproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Path.Homotopic.piproof · cited by 5
- Path.Homotopic.pi_liftstatement and proof · cited by 3
- Path.trans_pi_eq_pi_transstatement and proof · cited by 1
- Joined.piproof · cited by 1
- JoinedIn.piproof · cited by 1
- Path.Homotopic.comp_pi_eq_pi_compproof · cited by 0
- Path.pi_coestatement · cited by 0
- Path.Homotopic.piHomotopystatement · cited by 0
- Path.Homotopic.pi_projproof · cited by 0
- Path.Homotopic.proj_piproof · cited by 0