Theorems · Theorem · general topology
isPathConnected_range
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [PathConnectedSpace X]
{f : X → Y}, Continuous f → IsPathConnected (Set.range f)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- Set.image_univproof · cited by 322
- IsPathConnectedstatement and proof · cited by 65
- PathConnectedSpacestatement and proof · cited by 26
- IsPathConnected.imageproof · cited by 5
- isPathConnected_univproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Function.Surjective.pathConnectedSpaceproof · cited by 0