Theorems · Theorem · real analysis
nhdsLT_sup_nhdsGE
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] (a : α),
nhdsWithin a (Set.Iio a) ⊔ nhdsWithin a (Set.Ici a) = nhds a- Defined in
- Mathlib.Topology.Order.LeftRight
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceLinearOrder
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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- nhdsWithinstatement and proof · cited by 1,912
- Set.Iiostatement and proof · cited by 1,166
- Set.Icistatement and proof · cited by 1,070
- nhdsWithin_univproof · cited by 88
- nhdsWithin_unionproof · cited by 41
- Set.Iio_union_Iciproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- eventuallyEq_toIcoDiv_nhdsproof · cited by 2
- PredOrder.nhdsGE_eq_nhdsproof · cited by 1
- tendsto_measure_Iccproof · cited by 1
- ContinuousOn.comp_fract'proof · cited by 1