Theorems · Theorem · general topology
nhdsSet_Iio
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a : α},
nhdsSet (Set.Iio a) = Filter.principal (Set.Iio a)- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- Set.Iiostatement · cited by 1,166
- Filter.principalstatement · cited by 740
- OrderClosedTopologystatement and proof · cited by 445
- nhdsSetstatement · cited by 267
- isOpen_Iioproof · cited by 38
- IsOpen.nhdsSet_eqproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Iio_mem_nhdsSet_Icoproof · cited by 3