Theorems · Theorem · general topology
isOpen_Iio
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a : α}, IsOpen (Set.Iio a)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- IsOpenstatement and proof · cited by 2,400
- Set.Iiostatement · cited by 1,166
- ClosedIciTopologystatement and proof · cited by 156
- IsClosed.isOpen_complproof · cited by 126
- Set.compl_Iciproof · cited by 11
Cited by38
Results whose statement or proof uses this declaration.
- isOpen_Iooproof · cited by 54
- Iio_mem_nhdsproof · cited by 34
- measurableSet_Iioproof · cited by 12
- Metric.isOpen_thickeningproof · cited by 11
- borel_eq_generateFrom_Iioproof · cited by 6
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- Dense.exists_le'proof · cited by 4
- interior_Iioproof · cited by 3
- ENNReal.isOpenEmbedding_coeproof · cited by 3
- SuccOrder.isOpen_singleton_iffproof · cited by 3
- IsPreconnected.mapsTo_Ioi_or_Iioproof · cited by 2
- HasDerivWithinAt.limsup_norm_slope_leproof · cited by 2