Theorems · Definition · algebraic topology
ContinuousMap.Nullhomotopic
{X : Type u_1} → {Y : Type u_2} → [inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → C(X, Y) → PropA map is nullhomotopic if it is homotopic to a constant map.
- Defined in
- Mathlib.Topology.Homotopy.Contractible
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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
- ContinuousMapstatement and proof · cited by 2,491
- ContinuousMap.constproof · cited by 45
- ContinuousMap.Homotopicproof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- id_nullhomotopicstatement · cited by 2
- contractible_iff_id_nullhomotopicstatement and proof · cited by 1
- LocallyContractibleSpaceproof · cited by 1
- ContinuousMap.Nullhomotopic.comp_leftstatement and proof · cited by 0
- ContinuousMap.nullhomotopic_of_constantstatement · cited by 0
- ContinuousMap.Nullhomotopic.comp_rightstatement and proof · cited by 0
- nullhomotopic_of_indiscretestatement · cited by 0