Theorems · Theorem · general topology
not_tendsto_atTop_of_tendsto_nhds
∀ {α : Type u} {β : Type v} [inst : Preorder α] [NoTopOrder α] [inst_2 : TopologicalSpace α] [ClosedIciTopology α]
{a : α} {l : Filter β} [l.NeBot] {f : β → α}, Filter.Tendsto f l (nhds a) → ¬Filter.Tendsto f l Filter.atTop- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Filter.NeBotstatement and proof · cited by 853
- ClosedIciTopologystatement and proof · cited by 156
- NoTopOrderstatement and proof · cited by 50
- Filter.Tendsto.not_tendstoproof · cited by 14
- disjoint_nhds_atTopproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_const_const_iffproof · cited by 2
- tendsto_iff_tendsto_subseq_of_monotoneproof · cited by 2
- not_summable_of_ratio_norm_eventually_geproof · cited by 2
- FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendstoproof · cited by 1
- tendsto_nhds_iff_meromorphicOrderAt_nonnegproof · cited by 1
- tendsto_zero_iff_meromorphicOrderAt_posproof · cited by 0
- hoferproof · cited by 0
- tendsto_cobounded_iff_meromorphicOrderAt_negproof · cited by 0
- tendsto_ne_zero_iff_meromorphicOrderAt_eq_zeroproof · cited by 0