Theorems · Definition · algebraic topology
ContinuousMap.HomotopyEquiv.refl
(X : Type u) → [inst : TopologicalSpace X] → ContinuousMap.HomotopyEquiv X X
Any topological space is homotopy equivalent to itself.
- Defined in
- Mathlib.Topology.Homotopy.Equiv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 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.
Cites4
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
- Homeomorph.reflproof · cited by 25
- ContinuousMap.HomotopyEquivstatement · cited by 23
- Homeomorph.toHomotopyEquivproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMap.HomotopyEquiv.refl_applystatement and proof · cited by 0
- ContinuousMap.HomotopyEquiv.refl_symm_applystatement and proof · cited by 0
- Homeomorph.refl_toHomotopyEquivstatement · cited by 0