Theorems · Theorem · general topology
isPreconnected_range
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [PreconnectedSpace α] {f : α → β},
Continuous f → IsPreconnected (Set.range f)- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 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.
- 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
- Continuous.continuousOnproof · cited by 311
- IsPreconnectedstatement · cited by 205
- PreconnectedSpacestatement and proof · cited by 64
- PreconnectedSpace.isPreconnected_univproof · cited by 26
- IsPreconnected.imageproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- isConnected_rangeproof · cited by 3
- DenseRange.preconnectedSpaceproof · cited by 1