Theorems · Theorem · general topology
nhds_le_uniformity
∀ {α : Type ua} [inst : UniformSpace α] (x : α), nhds (x, x) ≤ uniformity αEntourages are neighborhoods of the diagonal.
- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- UniformSpacestatement and proof · cited by 2,040
- SProd.sprodproof · cited by 1,750
- uniformitystatement and proof · cited by 765
- Filter.mem_of_supersetproof · cited by 308
- SetRel.compproof · cited by 136
- UniformSpace.ballproof · cited by 113
- SetRel.IsSymmproof · cited by 93
- nhds_prod_eqproof · cited by 84
- Filter.prod_mem_prodproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- cauchy_nhdsproof · cited by 7
- Inseparable.nhds_le_uniformityproof · cited by 2
- iSup_nhds_le_uniformityproof · cited by 1
- Uniform.continuousAt_iff_prodproof · cited by 0
- Metric.isBounded_range_of_tendsto_cofiniteproof · cited by 0