Theorems · Theorem · general topology
Metric.isBounded_closure_of_isBounded
∀ {α : Type u} {s : Set α} [inst : PseudoMetricSpace α], Bornology.IsBounded s → Bornology.IsBounded (closure s)- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 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.
Cites11
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
- Realproof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- closurestatement and proof · cited by 1,254
- Bornology.IsBoundedstatement and proof · cited by 293
- isClosed_Iicproof · cited by 23
- Metric.isBounded_iffproof · cited by 15
- IsClosed.closure_subsetproof · cited by 11
- continuous_distproof · cited by 9
- map_mem_closure₂proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Bornology.IsBounded.closureproof · cited by 4