Theorems · Theorem · general topology
Iio_mem_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b : α},
b < a → Set.Iio a ∈ nhds b- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.Iiostatement · cited by 1,166
- IsOpen.mem_nhdsproof · cited by 470
- ClosedIciTopologystatement and proof · cited by 156
- isOpen_Iioproof · cited by 38
Cited by34
Results whose statement or proof uses this declaration.
- Ioo_mem_nhdsGTproof · cited by 20
- nhdsWithin_Ioo_eq_nhdsGTproof · cited by 9
- eventually_lt_nhdsproof · cited by 9
- Ico_mem_nhdsGEproof · cited by 8
- Iic_mem_nhdsproof · cited by 6
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- hasStrictDerivAt_abs_negproof · cited by 3
- Seminorm.bound_of_continuous_normedSpaceproof · cited by 3
- Manifold.exists_lt_locally_constant_of_riemannianEDist_ltproof · cited by 3
- not_summable_one_div_on_primesproof · cited by 2
- hasDerivAt_ofReal_cpow_const'proof · cited by 2