Theorems · Definition · algebraic topology
ContinuousMap.Homotopy.symm
{X : Type u} →
{Y : Type v} →
[inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → {f₀ f₁ : C(X, Y)} → f₀.Homotopy f₁ → f₁.Homotopy f₀Given a ContinuousMap.Homotopy f₀ f₁, we can define a ContinuousMap.Homotopy f₁ f₀ by
reversing the homotopy.
- Defined in
- Mathlib.Topology.Homotopy.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- ContinuousMapstatement and proof · cited by 2,491
- unitIntervalproof · cited by 607
- unitInterval.symmproof · cited by 69
- ContinuousMap.Homotopystatement and proof · cited by 65
Cited by8
Results whose statement or proof uses this declaration.
- ContinuousMap.HomotopyRel.symmproof · cited by 5
- ContinuousMap.HomotopyWith.symmproof · cited by 5
- TopCat.Homotopy.symmproof · cited by 4
- ContinuousMap.Homotopic.symmproof · cited by 3
- ContinuousMap.Homotopy.symm_symmstatement and proof · cited by 3
- ContinuousMap.Homotopy.symm_transstatement and proof · cited by 3
- ContinuousMap.Homotopy.symm_applystatement and proof · cited by 2
- ContinuousMap.Homotopy.symm_bijectivestatement and proof · cited by 0