Theorems · Theorem · general topology
Metric.infDist_pos_iff_notMem_closure
∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α}, s.Nonempty → (x ∉ closure s ↔ 0 < Metric.infDist x s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites10
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
- Set.Nonemptystatement and proof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- closurestatement · cited by 1,254
- Iff.notproof · cited by 489
- Metric.infDiststatement · cited by 68
- LE.le.lt_iff_ne'proof · cited by 16
- Metric.mem_closure_iff_infDist_zeroproof · cited by 5
- Metric.infDist_nonnegproof · cited by 3
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