Theorems · Theorem · general topology
interior_Ioc
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMaxOrder α] {a b : α}, interior (Set.Ioc a b) = Set.Ioo a b- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Ioostatement and proof · cited by 1,214
- Set.Iicproof · cited by 1,111
- Set.Iocstatement · cited by 971
- interiorstatement and proof · cited by 714
- DenselyOrderedstatement and proof · cited by 471
- NoMaxOrderstatement and proof · cited by 340
- interior_interproof · cited by 22
Cited by10
Results whose statement or proof uses this declaration.
- ConvexOn.continuousOn_Iocproof · cited by 2
- isMaxOn_Ioo_of_derivproof · cited by 1
- isMinOn_Ioo_of_derivproof · cited by 1
- isMaxOn_Ioc_of_derivproof · cited by 0
- isMaxOn_Ioi_of_derivproof · cited by 0
- isMinOn_Ioc_of_derivproof · cited by 0
- Ioc_mem_nhds_iffproof · cited by 0
- isMinOn_Ioi_of_derivproof · cited by 0
- uniqueDiffOn_Iocproof · cited by 0
- frontier_Iocproof · cited by 0