Theorems · Theorem · algebraic topology
id_nullhomotopic
∀ (X : Type u_1) [inst : TopologicalSpace X] [ContractibleSpace X], (ContinuousMap.id X).Nullhomotopic
- Defined in
- Mathlib.Topology.Homotopy.Contractible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- ContinuousMapproof · cited by 2,491
- ContinuousMap.compproof · cited by 181
- ContinuousMap.idstatement and proof · cited by 73
- ContinuousMap.constproof · cited by 45
- ContinuousMap.Homotopicproof · cited by 24
- ContinuousMap.HomotopyEquivproof · cited by 23
- ContractibleSpacestatement and proof · cited by 21
- ContinuousMap.HomotopyEquiv.toFunproof · cited by 12
- ContinuousMap.HomotopyEquiv.invFunproof · cited by 6
- ContinuousMap.Nullhomotopicstatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- contractible_iff_id_nullhomotopicproof · cited by 1
- StronglyLocallyContractibleSpace.locallyContractibleproof · cited by 0