Theorems · Theorem · general topology
interior_Iic
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMaxOrder α] {a : α}, interior (Set.Iic a) = Set.Iio a- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- OrderTopologystatement and proof · cited by 1,355
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement · cited by 1,111
- interiorstatement · cited by 714
- DenselyOrderedstatement and proof · cited by 471
- NoMaxOrderstatement and proof · cited by 340
- Set.nonempty_Ioiproof · cited by 10
- interior_Iic'proof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- interior_Iccproof · cited by 37
- interior_Iocproof · cited by 10
- geometric_hahn_banach_openproof · cited by 4
- uniqueDiffOn_Iicproof · cited by 3
- Complex.interior_setOfPred_im_leproof · cited by 1
- Complex.interior_setOfPred_re_leproof · cited by 1