Theorems · Theorem · general topology
Bornology.IsBounded.uniformContinuousOn_smul
∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] [inst_2 : Zero α]
[inst_3 : Zero β] [inst_4 : SMul α β] [IsBoundedSMul α β] {s : Set (α × β)},
Bornology.IsBounded s → UniformContinuousOn (Function.uncurry fun x1 x2 => x1 • x2) s- Defined in
- Mathlib.Topology.MetricSpace.Algebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- le_reflproof · cited by 2,061
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Metric.ballproof · cited by 735
- add_le_addproof · cited by 666
Cited by1
Results whose statement or proof uses this declaration.
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4