Theorems · Theorem · general topology
IsPreconnected.Iio_csSup_subset
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α] {s : Set α},
IsPreconnected s → ¬BddBelow s → BddAbove s → Set.Iio (sSup s) ⊆ s- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.Iiostatement · cited by 1,166
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- BddBelowstatement and proof · cited by 401
- IsPreconnectedstatement and proof · cited by 205
- IsPreconnected.Ioi_csInf_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsPreconnected.mem_intervalsproof · cited by 1