Theorems · Theorem · general topology
comap_dist_left_atTop_eq_cocompact
∀ {α : Type u} [inst : PseudoMetricSpace α] [ProperSpace α] (x : α),
Filter.comap (dist x) Filter.atTop = Filter.cocompact α- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceProperSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement · cited by 8,121
- Filter.atTopstatement · cited by 2,405
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Filter.comapstatement · cited by 546
- ProperSpacestatement and proof · cited by 190
- Filter.cocompactstatement and proof · cited by 141
- Metric.cobounded_eq_cocompactproof · cited by 8
- Metric.comap_dist_left_atTopproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1