Theorems · Theorem · general topology
isConnected_range
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [ConnectedSpace α] {f : α → β},
Continuous f → IsConnected (Set.range f)- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsConnectedstatement · cited by 116
- Set.range_nonemptyproof · cited by 84
- ConnectedSpacestatement and proof · cited by 37
- isPreconnected_rangeproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- pathComponent_subset_componentproof · cited by 2
- Function.Surjective.connectedSpaceproof · cited by 1
- Continuous.exists_lift_sigmaproof · cited by 1