Theorems · Theorem · general topology
LocallyPathConnectedSpace.coinduced
∀ {X : Type u_1} [inst : TopologicalSpace X] [LocallyPathConnectedSpace X] {Y : Type u_4} (f : X → Y),
LocallyPathConnectedSpace YAny topology coinduced by a locally path-connected topology is locally path-connected.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- LE.le.transproof · cited by 3,151
- Continuousproof · cited by 2,592
- IsOpenproof · cited by 2,400
- Set.image_subset_iffproof · cited by 203
- Set.image_monoproof · cited by 197
- IsOpen.preimageproof · cited by 147
- Set.preimage_monoproof · cited by 95
- Set.image_preimage_subsetproof · cited by 75
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsQuotientMap.locallyPathConnectedSpaceproof · cited by 2
- LocPathConnectedSpace.coinducedproof · cited by 0