Theorems · Theorem · general topology
isOpen_Ioi
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIicTopology α] {a : α}, IsOpen (Set.Ioi a)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 43 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.Ioistatement · cited by 1,463
- IsClosed.isOpen_complproof · cited by 126
- ClosedIicTopologystatement and proof · cited by 115
- Set.compl_Iicproof · cited by 10
Cited by43
Results whose statement or proof uses this declaration.
- measurableSet_Ioiproof · cited by 83
- isOpen_Iooproof · cited by 54
- Ioi_mem_nhdsproof · cited by 27
- Complex.differentiableAt_Gammaproof · cited by 8
- borel_eq_generateFrom_Iioproof · cited by 6
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- interior_Ioiproof · cited by 4
- LowerSemicontinuousWithinAt.add'proof · cited by 4
- contentRegular_rieszContentproof · cited by 3
- IsPreconnected.mapsTo_Ioi_or_Iioproof · cited by 2
- nhdsSet_Ioiproof · cited by 2
- Real.isOpenEmbedding_expproof · cited by 2