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Theorems · Theorem · general topology

Metric.AreSeparated.mono

∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {s t s' t' : Set X},
  s ⊆ s' → t ⊆ t' → Metric.AreSeparated s' t' → Metric.AreSeparated s t
Defined in
Mathlib.Topology.MetricSpace.MetricSeparated
Cited by
3 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.

MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodory · cited by 1IsMetric.borel_le_carathe…Metric.AreSeparated.mono_left · cited by 1AreSeparated.mono_leftMetric.AreSeparated.mono_right · cited by 0AreSeparated.mono_rightSet · cited by 53352SetENNReal · cited by 9879ENNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistMetric.AreSeparated · cited by 23Metric.AreSeparatedAreSeparated.monoCITED BYCITES

Cites5

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Cited by3

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