Theorems · Theorem · general topology
Metric.exists_isBounded_image_of_tendsto
∀ {α : Type u_3} {β : Type u_4} [inst : PseudoMetricSpace β] {l : Filter α} {f : α → β} {x : β},
Filter.Tendsto f l (nhds x) → ∃ s ∈ l, Bornology.IsBounded (f '' s)- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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.
- Setstatement · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.imagestatement · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Bornology.IsBoundedstatement · cited by 293
- Filter.basis_setsproof · cited by 105
- Filter.HasBasis.mapproof · cited by 51
- Disjoint.mono_leftproof · cited by 50
- Filter.HasBasis.disjoint_iff_leftproof · cited by 11
- Metric.disjoint_nhds_coboundedproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.eq_const_of_tendsto_cocompactproof · cited by 1