Theorems · Theorem · general topology
Metric.infDist_zero_of_mem
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α}, x ∈ s → Metric.infDist x s = 0The minimal distance of a point to a set containing it vanishes.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.toRealproof · cited by 859
- Metric.infDiststatement · cited by 68
- Metric.infEDist_zero_of_memproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Metric.infDist_zero_of_mem_closureproof · cited by 1