Theorems · Theorem · algebraic topology
SimplyConnectedSpace.paths_homotopic
∀ {X : Type u_3} [inst : TopologicalSpace X] [SimplyConnectedSpace X] {x y : X} (p₁ p₂ : Path x y), p₁.Homotopic p₂In a simply connected space, any two paths are homotopic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Quotient.eqproof · cited by 50
- Path.Homotopicstatement · cited by 28
- SimplyConnectedSpacestatement and proof · cited by 19
- Path.Homotopic.setoidproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- IsCoveringMap.existsUnique_continuousMap_liftsproof · cited by 1