Theorems · Theorem · general topology
tendsto_nhds_unique_dist
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] {f : β → α} {l : Filter β} {x y : α} [l.NeBot],
Filter.Tendsto f l (nhds x) → Filter.Tendsto f l (nhds y) → dist x y = 0A weaker version of tendsto_nhds_unique for PseudoMetricSpace.
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- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Filter.NeBotstatement and proof · cited by 853
- tendsto_nhds_unique_inseparableproof · cited by 10
- Inseparable.dist_eq_zeroproof · cited by 1
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