Theorems · Theorem · general topology
Metric.isBounded_range_of_tendsto_cofinite_uniformity
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] {f : β → α},
Filter.Tendsto (Prod.map f f) (Filter.cofinite ×ˢ Filter.cofinite) (uniformity α) → Bornology.IsBounded (Set.range f)- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Set.rangestatement · cited by 4,705
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complproof · cited by 2,925
- Set.Finiteproof · cited by 1,814
- SProd.sprodstatement and proof · cited by 1,750
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- le_of_ltproof · cited by 1,175
- uniformitystatement and proof · cited by 765
Cited by2
Results whose statement or proof uses this declaration.
- Metric.isBounded_range_of_cauchy_map_cofiniteproof · cited by 1
- Metric.isBounded_range_of_tendsto_cofiniteproof · cited by 0