Theorems · Theorem · general topology
isPreconnected_Ioc
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
[DenselyOrdered α] {a b : α}, IsPreconnected (Set.Ioc a b)- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 5 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.
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
- OrderTopologystatement and proof · cited by 1,355
- Set.Iocstatement · cited by 971
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- DenselyOrderedstatement and proof · cited by 471
- IsPreconnectedstatement · cited by 205
- Set.OrdConnected.isPreconnectedproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- intermediate_value_Iocproof · cited by 2
- intermediate_value_Ioc'proof · cited by 1
- isPreconnected_uIocproof · cited by 1
- isConnected_Iocproof · cited by 1
- exists_eq_interval_average_of_measureproof · cited by 0