Theorems · Theorem · general topology
ConditionallyCompleteLinearOrder.isCompact_Icc
∀ {α : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α] (a b : α),
IsCompact (Set.Icc a b)A closed interval in a conditionally complete linear order is compact.
Also see general API on CompactIccSpace.
- Defined in
- Mathlib.Topology.Order.IsLUB
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.Iccstatement and proof · cited by 1,702
- iInfproof · cited by 1,690
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Set.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- IsCompactstatement · cited by 1,282
- Set.Iioproof · cited by 1,166
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