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Theorems · Theorem · general topology

Metric.disjoint_closedEBall_of_lt_infEDist

∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s : Set α} {r : ENNReal},
  r < Metric.infEDist x s → Disjoint (Metric.closedEBall x r) s
Defined in
Mathlib.Topology.MetricSpace.HausdorffDistance
Cited by
1 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

EMetric.disjoint_closedBall_of_lt_infEdist · cited by 0EMetric.disjoint_closedBa…Set · cited by 53352SetENNReal · cited by 9879ENNRealDisjoint · cited by 2201DisjointPseudoEMetricSpace · cited by 1536PseudoEMetricSpacelt_irrefl · cited by 190lt_irreflMetric.infEDist · cited by 147Metric.infEDistSet.disjoint_left · cited by 121Set.disjoint_leftMetric.closedEBall · cited by 107Metric.closedEBallPseudoEMetricSpace.edist_comm · cited by 52PseudoEMetricSpace.edist_…Metric.infEDist_le_edist_of_mem · cited by 13Metric.infEDist_le_edist_…Metric.mem_closedEBall · cited by 7Metric.mem_closedEBallMetric.disjoint_closedEBall_o…CITED BYCITES

Cites11

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Cited by1

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