Theorems · Theorem · general topology
Metric.eball_top
∀ {α : Type u} [inst : PseudoMetricSpace α] (x : α), Metric.eball x ⊤ = Set.univ- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 147 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.univstatement · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.eballstatement · cited by 294
- Set.eq_univ_of_forallproof · cited by 80
- edist_lt_topproof · cited by 32
Cited by7
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.cpolynomialAtproof · cited by 3
- convex_eballproof · cited by 3
- ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinearproof · cited by 3
- Real.volume_eballproof · cited by 1
- FormalMultilinearSeries.continuousOn_of_finiteproof · cited by 0
- analyticWithinAt_of_singleton_memproof · cited by 0
- Metric.emetric_ball_topproof · cited by 0