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Theorems · Theorem · general topology

Metric.IsCover.mono_radius

∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ε δ : NNReal} {s N : Set X},
  ε ≤ δ → Metric.IsCover ε s N → Metric.IsCover δ s N
Defined in
Mathlib.Topology.MetricSpace.Cover
Cited by
2 results in Mathlib
Foundations
Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Metric.externalCoveringNumber_anti · cited by 0Metric.externalCoveringNu…Metric.coveringNumber_anti · cited by 0Metric.coveringNumber_antiSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredNNReal · cited by 4310NNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealle_trans · cited by 985le_transEDist.edist · cited by 735EDist.edistMetric.IsCover · cited by 51Metric.IsCoverSetRel.IsCover.mono_entourage · cited by 3IsCover.mono_entourageIsCover.mono_radiusCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.