Theorems · Theorem · general topology
denselyOrdered_of_preconnectedSpace
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [PreconnectedSpace α],
DenselyOrdered α- Defined in
- Mathlib.Topology.Order.IntermediateValue
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptyproof · cited by 2,627
- Set.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- DenselyOrderedstatement · cited by 471
- Set.mem_Ioiproof · cited by 80
- PreconnectedSpacestatement and proof · cited by 64
- Set.mem_Iioproof · cited by 49
- isOpen_Iio'proof · cited by 4
- isOpen_Ioi'proof · cited by 3
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