Theorems · Theorem · general topology
Metric.dist_mem_uniformity
∀ {α : Type u} [inst : PseudoMetricSpace α] {ε : ℝ}, 0 < ε → {p | dist p.1 p.2 < ε} ∈ uniformity αA constant size neighborhood of the diagonal is an entourage.
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 115 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement · cited by 8,121
- Set.ofPredstatement · cited by 6,101
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- uniformitystatement · cited by 765
- Metric.mem_uniformity_distproof · cited by 8
Cited by23
Results whose statement or proof uses this declaration.
- Metric.tendstoUniformlyOn_iffproof · cited by 14
- Metric.isClosedEmbedding_of_pairwise_le_distproof · cited by 5
- Metric.isUniformEmbedding_bot_of_pairwise_le_distproof · cited by 4
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- Metric.tendstoUniformlyOnFilter_iffproof · cited by 3
- TendstoLocallyUniformlyOn.inv₀_of_disjointproof · cited by 3
- BoundedContinuousFunction.tendsto_iff_tendstoUniformlyproof · cited by 2
- continuousOn_integral_bilinear_of_locally_integrable_of_compact_supportproof · cited by 2
- Metric.complete_of_convergent_controlled_sequencesproof · cited by 2
- controlled_sum_of_mem_closureproof · cited by 2
- intervalIntegral.continuous_parametric_primitive_of_continuousproof · cited by 1