Theorems · Definition · algebraic topology
Path.Homotopic
{X : Type u} → [inst : TopologicalSpace X] → {x₀ x₁ : X} → Path x₀ x₁ → Path x₀ x₁ → PropTwo paths p₀ and p₁ are Path.Homotopic if there exists a Homotopy between them.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 116 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.
Cites3
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.Homotopyproof · cited by 21
Cited by29
Results whose statement or proof uses this declaration.
- Path.Homotopic.setoidproof · cited by 14
- Path.Homotopic.Quotient.eqstatement · cited by 3
- Path.Homotopic.reflstatement · cited by 2
- Path.Homotopic.hcompstatement and proof · cited by 1
- Path.Homotopic.refl_transstatement · cited by 1
- Path.Homotopic.symmstatement and proof · cited by 1
- Path.Homotopic.symm_transstatement · cited by 1
- Path.Homotopic.transstatement and proof · cited by 1
- Path.Homotopic.trans_assocstatement · cited by 1
- Path.Homotopic.trans_reflstatement · cited by 1
- Path.Homotopic.trans_symmstatement · cited by 1
- SimplyConnectedSpace.paths_homotopicstatement · cited by 1