Theorems · Theorem · general topology
exists_seq_strictMono_tendsto
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMinOrder α] [FirstCountableTopology α] (x : α),
∃ u, StrictMono u ∧ (∀ (n : ℕ), u n < x) ∧ Filter.Tendsto u Filter.atTop (nhds x)- Defined in
- Mathlib.Topology.Order.IsLUB
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- OrderTopologystatement and proof · cited by 1,355
- Set.Iooproof · cited by 1,214
- StrictMonostatement and proof · cited by 706
- DenselyOrderedstatement and proof · cited by 471
- NoMinOrderstatement and proof · cited by 247
- FirstCountableTopologystatement and proof · cited by 106
- NoMinOrder.exists_ltproof · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- exists_seq_strictAnti_tendstoproof · cited by 18
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1
- exists_seq_strictMono_tendsto_nhdsWithinproof · cited by 1