Theorems · Theorem · general topology
ge_mem_nhds
∀ {α : Type u} [ts : TopologicalSpace α] [inst : Preorder α] [OrderTopology α] {a b : α},
b < a → ∀ᶠ (x : α) in nhds b, x ≤ a- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 8 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.
Cites8
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
- Preorderstatement and proof · cited by 7,952
- nhdsstatement · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- OrderTopologystatement and proof · cited by 1,355
- le_of_ltproof · cited by 1,175
- Filter.Eventually.monoproof · cited by 646
- gt_mem_nhdsproof · cited by 37
Cited by8
Results whose statement or proof uses this declaration.
- PhragmenLindelof.horizontal_stripproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- Irrational.eventually_forall_le_dist_cast_divproof · cited by 2
- limsSup_nhdsproof · cited by 2
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- ENNReal.tendsto_subproof · cited by 2
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- MeasureTheory.AECover.integrable_of_lintegral_enorm_tendstoproof · cited by 1