Theorems · Theorem · algebraic topology
Path.Homotopy.source
∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ : X} {p₀ p₁ : Path x₀ x₁} (F : p₀.Homotopy p₁) (t : ↑unitInterval),
F (t, 0) = x₀- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 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.
Cites12
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 and proof · cited by 7,166
- ContinuousMapstatement · cited by 2,491
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- Path.toContinuousMapstatement · cited by 27
- Path.sourceproof · cited by 26
- Path.Homotopystatement and proof · cited by 21
- ContinuousMap.HomotopyRel.eq_fstproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- isSimplyConnected_iff_exists_homotopy_refl_forall_memproof · cited by 0