Theorems · Theorem · general topology
Metric.isBounded_Ioo
∀ {α : Type u} [inst : PseudoMetricSpace α] [inst_1 : Preorder α] [CompactIccSpace α] (a b : α),
Bornology.IsBounded (Set.Ioo a b)- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Preorderstatement and proof · cited by 7,952
- PseudoMetricSpacestatement and proof · cited by 1,550
- Set.Ioostatement · cited by 1,214
- Bornology.IsBoundedstatement · cited by 293
- CompactIccSpacestatement and proof · cited by 96
- TotallyBounded.isBoundedproof · cited by 5
- totallyBounded_Iooproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Real.ediam_Iooproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- ContinuousMap.exists_extension_forall_mem_of_isClosedEmbeddingproof · cited by 1
- closure_openSegmentproof · cited by 0
- Metric.isBounded_of_abs_ltproof · cited by 0