Theorems · Theorem · general topology
Metric.mem_closure_range_iff_nat
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] {e : β → α} {a : α},
a ∈ closure (Set.range e) ↔ ∀ (n : ℕ), ∃ k, dist a (e k) < 1 / (↑n + 1)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.rangestatement and proof · cited by 4,705
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- closurestatement · cited by 1,254
- dist_commproof · cited by 188
- mem_closure_iff_nhds_basisproof · cited by 13
- Metric.nhds_basis_ball_inv_nat_succproof · cited by 1
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