Theorems · Definition · algebraic topology
Path.Homotopy.refl
{X : Type u} → [inst : TopologicalSpace X] → {x₀ x₁ : X} → (p : Path x₀ x₁) → p.Homotopy pGiven a path p, we can define a Homotopy p p by F (t, x) = p x.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 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.
Cites5
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
- Pathstatement and proof · cited by 318
- Path.toContinuousMapproof · cited by 27
- Path.Homotopystatement · cited by 21
- ContinuousMap.HomotopyRel.reflproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Path.Homotopic.reflproof · cited by 2
- Path.Homotopy.concatproof · cited by 1
- Path.Homotopy.concatSubpathproof · cited by 1
- Path.Homotopy.refl_applystatement and proof · cited by 0