Theorems · Definition · general topology
Path.extend
{X : Type u_1} → [inst : TopologicalSpace X] → {x y : X} → Path x y → C(ℝ, X)A continuous map extending a path to ℝ, constant before 0 and after 1.
- Defined in
- Mathlib.Topology.Path
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 121 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement · cited by 2,491
- Pathstatement and proof · cited by 318
- Set.IccExtendproof · cited by 26
Cited by56
Results whose statement or proof uses this declaration.
- Path.transproof · cited by 54
- Path.extend_applystatement · cited by 9
- Path.trans_applyproof · cited by 9
- curveIntegralFun_def'statement and proof · cited by 8
- Path.truncatestatement and proof · cited by 7
- curveIntegralFun_defstatement and proof · cited by 5
- Path.extend_extends'statement · cited by 3
- Path.extend_rangestatement · cited by 3
- Path.extend_trans_of_le_halfstatement and proof · cited by 3
- Path.extend_zerostatement · cited by 3
- Path.Homotopy.hcompproof · cited by 3
- curveIntegralFun_addproof · cited by 3