Theorems · Theorem · general topology
isPreconnected_iff_ordConnected
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
[DenselyOrdered α] {s : Set α}, IsPreconnected s ↔ s.OrdConnected- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- DenselyOrderedstatement and proof · cited by 471
- IsPreconnectedstatement · cited by 205
- Set.OrdConnectedstatement · cited by 161
- Set.OrdConnected.isPreconnectedproof · cited by 9
- IsPreconnected.ordConnectedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.convex_iff_isPreconnectedproof · cited by 2