Theorems · Definition · algebraic topology
ContinuousMap.HomotopyRel
{X : Type u} →
{Y : Type v} →
[inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → C(X, Y) → C(X, Y) → Set X → Type (max u v)A HomotopyRel f₀ f₁ S is a homotopy between f₀ and f₁ which is fixed on the points in S.
- Defined in
- Mathlib.Topology.Homotopy.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
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.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement and proof · cited by 2,491
- ContinuousMap.HomotopyWithproof · cited by 33
Cited by39
Results whose statement or proof uses this declaration.
- Path.Homotopyproof · cited by 21
- ContinuousMap.HomotopicRelproof · cited by 11
- ContinuousMap.HomotopyRel.eq_fststatement and proof · cited by 8
- ContinuousMap.HomotopyRel.symmstatement and proof · cited by 5
- ContinuousMap.HomotopyRel.compContinuousMapstatement and proof · cited by 3
- ContinuousMap.HomotopyRel.transstatement and proof · cited by 3
- IsCoveringMap.liftHomotopyRelstatement and proof · cited by 2
- ContinuousMap.HomotopyRel.eq_sndstatement and proof · cited by 2
- ContinuousMap.HomotopyRel.reflstatement · cited by 2
- ContinuousMap.HomotopyRel.symm_symmstatement and proof · cited by 2
- GenLoop.homotopyTostatement and proof · cited by 2
- ContinuousMap.HomotopicRel.comp_continuousMapproof · cited by 1