Mathlib Map

Theorems · Theorem · general topology

Metric.mem_thickening_iff_infDist_lt

∀ {δ : ℝ} {X : Type u} [inst : PseudoMetricSpace X] {E : Set X} {x : X},
  E.Nonempty → (x ∈ Metric.thickening δ E ↔ Metric.infDist x E < δ)
Defined in
Mathlib.Topology.MetricSpace.Thickening
Cited by
2 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Bornology.IsBounded.thickening · cited by 1IsBounded.thickeningMetric.tendsto_nhdsSet · cited by 0Metric.tendsto_nhdsSetSet · cited by 53352SetReal · cited by 25697RealSet.Nonempty · cited by 2627Set.NonemptyPseudoMetricSpace · cited by 1550PseudoMetricSpaceMetric.thickening · cited by 130Metric.thickeningMetric.infDist · cited by 68Metric.infDistMetric.infEDist_ne_top · cited by 8Metric.infEDist_ne_topENNReal.lt_ofReal_iff_toReal_lt · cited by 7ENNReal.lt_ofReal_iff_toR…Metric.mem_thickening_iff_inf…CITED BYCITES

Cites8

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.