Theorems · Theorem · general topology
Path.range_segment
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [inst_3 : ContinuousAdd E]
[inst_4 : ContinuousSMul ℝ E] (a b : E), Set.range ⇑(Path.segment a b) = segment ℝ a b- Defined in
- Mathlib.Analysis.Convex.PathConnected
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Set.Iccproof · cited by 1,702
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- unitIntervalstatement · cited by 607
Cited by3
Results whose statement or proof uses this declaration.
- Circle.range_pathproof · cited by 2
- JoinedIn.of_segment_subsetproof · cited by 2
- Circle.path_injective_of_neproof · cited by 1