Theorems · Definition · general topology
Path.map
{X : Type u_1} →
{Y : Type u_2} →
[inst : TopologicalSpace X] →
[inst_1 : TopologicalSpace Y] → {x y : X} → Path x y → {f : X → Y} → Continuous f → Path (f x) (f y)Image of a path from x to y by a continuous map
- Defined in
- Mathlib.Topology.Path
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- Pathstatement and proof · cited by 318
- Path.map'proof · cited by 4
Cited by28
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotient.mapproof · cited by 19
- Circle.pathproof · cited by 16
- Path.map_coestatement and proof · cited by 6
- Path.addproof · cited by 5
- Path.Homotopy.mapstatement · cited by 4
- Path.Homotopic.Quotient.mk_mapstatement · cited by 3
- Path.invproof · cited by 3
- Path.mulproof · cited by 3
- Path.negproof · cited by 3
- Joined.mapproof · cited by 2
- IsCoveringMap.monodromy_mapproof · cited by 2
- IsQuotientCoveringMap.fundamentalGroupToMulOpposite_surjectiveproof · cited by 1