Theorems · Theorem · general topology
isConnected_Iio
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
[DenselyOrdered α] {a : α} [NoMinOrder α], IsConnected (Set.Iio a)- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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
- OrderTopologystatement and proof · cited by 1,355
- Set.Iiostatement · cited by 1,166
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- DenselyOrderedstatement and proof · cited by 471
- NoMinOrderstatement and proof · cited by 247
- IsConnectedstatement · cited by 116
- Set.nonempty_Iioproof · cited by 10
- isPreconnected_Iioproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AffineSubspace.isConnected_setOfPred_sOppSideproof · cited by 2