Theorems · Theorem · general topology
Path.image_extend_of_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} (γ : Path x y) {s : Set ℝ},
unitInterval ⊆ s → ⇑γ.extend '' s = Set.range ⇑γ- Defined in
- Mathlib.Topology.Path
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 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.
Cites16
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 and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement · cited by 5,609
- Set.rangestatement · cited by 4,705
- ContinuousMapstatement · cited by 2,491
- unitIntervalstatement and proof · cited by 607
- LE.le.antisymmproof · cited by 507
- Pathstatement and proof · cited by 318
- Set.range_subset_iffproof · cited by 99
Cited by1
Results whose statement or proof uses this declaration.
- Path.trans_rangeproof · cited by 1