Theorems · Theorem · general topology
IsCompact.exists_infEdist_eq_edist
Deprecated since 2026-01-08Use IsCompact.exists_infEDist_eq_edist instead.
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α},
IsCompact s → s.Nonempty → ∀ (x : α), ∃ y ∈ s, Metric.infEDist x s = edist x yAlias of IsCompact.exists_infEDist_eq_edist.
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- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- Set.Nonemptystatement · cited by 2,627
- PseudoEMetricSpacestatement · cited by 1,536
- IsCompactstatement · cited by 1,282
- EDist.ediststatement · cited by 735
- Metric.infEDiststatement · cited by 147
- IsCompact.exists_infEDist_eq_edistproof · cited by 3
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