Theorems · Theorem · general topology
Path.map_coe
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x y : X} (γ : Path x y)
{f : X → Y} (h : Continuous f), ⇑(γ.map h) = f ∘ ⇑γ- Defined in
- Mathlib.Topology.Path
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Continuousstatement and proof · cited by 2,592
- unitIntervalstatement and proof · cited by 607
- Pathstatement and proof · cited by 318
- Path.mapstatement and proof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- Circle.path_selfproof · cited by 2
- Circle.path_applyproof · cited by 1
- Path.map_transproof · cited by 1
- joinedIn_iff_joinedproof · cited by 0
- isSimplyConnected_iff_exists_homotopy_refl_forall_memproof · cited by 0
- Path.Homotopic.map_trans_evalAtproof · cited by 0