Theorems · Theorem · general topology
eq_Icc_of_connected_compact
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
{s : Set α}, IsConnected s → IsCompact s → s = Set.Icc (sInf s) (sSup s)- Defined in
- Mathlib.Topology.Order.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.Iccstatement · cited by 1,702
- OrderTopologystatement and proof · cited by 1,355
- IsCompactstatement and proof · cited by 1,282
- SupSet.sSupstatement · cited by 954
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- IsConnectedstatement and proof · cited by 116
- IsCompact.isClosedproof · cited by 77
- IsCompact.bddBelowproof · cited by 8
- IsCompact.bddAboveproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousOn.image_Iccproof · cited by 3