Theorems · Theorem · general topology
eventually_lt_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b : α},
a < b → ∀ᶠ (x : α) in nhds a, x < b- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- ClosedIciTopologystatement and proof · cited by 156
- Iio_mem_nhdsproof · cited by 34
Cited by9
Results whose statement or proof uses this declaration.
- Filter.Tendsto.eventually_lt_constproof · cited by 13
- ConvexOn.le_slope_of_hasDerivWithinAt_Ioiproof · cited by 5
- Monotone.tendstoLocallyUniformly_of_forall_tendstoproof · cited by 4
- Metric.eventually_notMem_cthickening_of_infEDist_posproof · cited by 3
- Metric.eventually_notMem_thickening_of_infEDist_posproof · cited by 3
- ConvexOn.continuousOn_tfaeproof · cited by 3
- MeasureTheory.aecover_Ioi_of_Ioiproof · cited by 3
- lowerSemicontinuousOn_iff_isClosed_epigraphproof · cited by 2
- Metric.eventually_nhds_zero_forall_closedEBall_subsetproof · cited by 2