Theorems · Theorem · general topology
not_tendsto_nhds_of_tendsto_atTop
∀ {α : Type u} {β : Type v} [inst : Preorder α] [NoTopOrder α] [inst_2 : TopologicalSpace α] [ClosedIciTopology α]
{l : Filter β} [l.NeBot] {f : β → α}, Filter.Tendsto f l Filter.atTop → ∀ (a : α), ¬Filter.Tendsto f l (nhds a)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 7 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.
Cites12
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 · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.NeBotstatement and proof · cited by 853
- ClosedIciTopologystatement and proof · cited by 156
- Disjoint.symmproof · cited by 125
- NoTopOrderstatement and proof · cited by 50
- Filter.Tendsto.not_tendstoproof · cited by 14
- disjoint_nhds_atTopproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- tendsto_pow_atTop_nhds_zero_iffproof · cited by 2
- NNReal.not_summable_iff_tendsto_nat_atTopproof · cited by 2
- Complex.continuousAt_tanproof · cited by 2
- Real.continuousAt_tanproof · cited by 2
- Real.not_differentiableAt_rpow_const_zeroproof · cited by 1
- tendsto_const_mul_pow_nhds_iff'proof · cited by 0
- Real.continuousAt_logb_iffproof · cited by 0