Theorems · Theorem · general topology
Path.extend_apply
∀ {X : Type u_1} [inst : TopologicalSpace X] {a b : X} (γ : Path a b) {t : ℝ} (ht : t ∈ Set.Icc 0 1),
γ.extend t = γ ⟨t, ht⟩- Defined in
- Mathlib.Topology.Path
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 122 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- ContinuousMapstatement · cited by 2,491
- Set.Iccstatement and proof · cited by 1,702
- unitIntervalstatement · cited by 607
- Pathstatement and proof · cited by 318
- Path.extendstatement · cited by 52
- Set.IccExtend_of_memproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Path.trans_applyproof · cited by 9
- Path.extend_trans_of_le_halfproof · cited by 3
- Path.extend_zeroproof · cited by 3
- Path.extend_oneproof · cited by 2
- Path.trans_continuous_familyproof · cited by 1
- Path.eqOn_extend_segmentproof · cited by 1
- Path.ofLine_extendproof · cited by 0
- Path.Homotopy.hcomp_applyproof · cited by 0
- Path.Homotopy.hcomp_halfproof · cited by 0