Theorems · Theorem · general topology
Dense.topology_eq_generateFrom
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α] {s : Set α},
Dense s → inst = TopologicalSpace.generateFrom (Set.Ioi '' s ∪ Set.Iio '' s)- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- IsOpenproof · cited by 2,400
- le_antisymmproof · cited by 2,068
- Set.Ioistatement and proof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Iiostatement and proof · cited by 1,166
- DenselyOrderedstatement and proof · cited by 471
- Set.mem_image_of_memproof · cited by 371
Cited by1
Results whose statement or proof uses this declaration.
- SecondCountableTopology.of_separableSpace_orderTopologyproof · cited by 0