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Theorems · Theorem · general topology

eventually_le_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
8 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceLinearOrderClosedIciTopology
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Around this declaration

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Filter.Tendsto.eventually_le_const · cited by 15Tendsto.eventually_le_con…ConvexOn.continuousOn_tfae · cited by 3ConvexOn.continuousOn_tfaeReal.tendstoLocallyUniformlyOn_rpow_sub_one_log · cited by 2Real.tendstoLocallyUnifor…curveIntegralFun_trans_of_lt_half · cited by 2curveIntegralFun_trans_of…Asymptotics.Filter.Tendsto.isBigOTVS_one · cited by 1Tendsto.isBigOTVS_oneModularFormClass.qExpansion_isBigO · cited by 1ModularFormClass.qExpansi…WeakFEPair.hf_zero' · cited by 1WeakFEPair.hf_zero'Vitali.exists_disjoint_covering_ae · cited by 1Vitali.exists_disjoint_co…TopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrdernhds · cited by 5554nhdsFilter.Eventually · cited by 3134Filter.EventuallyClosedIciTopology · cited by 156ClosedIciTopologyIic_mem_nhds · cited by 6Iic_mem_nhdseventually_le_nhdsCITED BYCITES

Cites6

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Cited by8

Results whose statement or proof uses this declaration.