Theorems · Theorem · general topology
interior_Ici
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMinOrder α] {a : α}, interior (Set.Ici a) = Set.Ioi a- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 85 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
- Set.Ioistatement · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Icistatement · cited by 1,070
- interiorstatement · cited by 714
- DenselyOrderedstatement and proof · cited by 471
- NoMinOrderstatement and proof · cited by 247
- interior_Ici'proof · cited by 13
- Set.nonempty_Iioproof · cited by 10
Cited by14
Results whose statement or proof uses this declaration.
- interior_Iccproof · cited by 37
- interior_Icoproof · cited by 12
- uniqueDiffOn_Iciproof · cited by 4
- interior_halfSpaceproof · cited by 2
- geometric_hahn_banach_open_openproof · cited by 2
- Real.sinh_sub_id_strictMonoproof · cited by 2
- Real.cosh_strictMonoOnproof · cited by 2
- Complex.interior_setOfPred_le_improof · cited by 1
- Complex.interior_setOfPred_le_reproof · cited by 1
- AffineBasis.interior_convexHullproof · cited by 1
- ModularGroup.fdo_eq_interior_fdproof · cited by 0
- strictConvexOn_powproof · cited by 0