Theorems · Theorem · general topology
isConnected_Ioi
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
[DenselyOrdered α] {a : α} [NoMaxOrder α], IsConnected (Set.Ioi a)- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 2 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
- Set.Ioistatement · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- DenselyOrderedstatement and proof · cited by 471
- NoMaxOrderstatement and proof · cited by 340
- IsConnectedstatement · cited by 116
- Set.nonempty_Ioiproof · cited by 10
- isPreconnected_Ioiproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AffineSubspace.isConnected_setOfPred_sSameSideproof · cited by 3
- isConnected_setOfPred_sameRay_and_ne_zeroproof · cited by 2