Theorems · Theorem · general topology
Metric.boundedSpace_iff_edist
∀ {α : Type u} [inst : PseudoMetricSpace α], BoundedSpace α ↔ ∃ C, ∀ (a b : α), edist a b ≤ ↑C- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 117 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- ENNReal.ofNNRealstatement · cited by 1,279
- EDist.ediststatement · cited by 735
- NNDist.nndistproof · cited by 235
- BoundedSpacestatement · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- MemHolder.of_leproof · cited by 3
- HolderOnWith.exists_holderOnWith_of_le'proof · cited by 0
- MemHolder.of_le'proof · cited by 0