Theorems · Theorem · general topology
inseparable_iff_clusterPt_uniformity
∀ {α : Type u} [inst : UniformSpace α] {x y : α}, Inseparable x y ↔ ClusterPt (x, y) (uniformity α)- Defined in
- Mathlib.Topology.UniformSpace.Separation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- uniformitystatement and proof · cited by 765
- Filter.principalproof · cited by 740
- SetRelproof · cited by 581
- Inseparablestatement and proof · cited by 160
- ClusterPtstatement and proof · cited by 138
- Filter.le_principal_iffproof · cited by 87
- ClusterPt.monoproof · cited by 30
- Filter.HasBasis.inseparable_iff_uniformityproof · cited by 5
- uniformity_hasBasis_closedproof · cited by 4
- Inseparable.nhds_le_uniformityproof · cited by 2
- ClusterPt.of_nhds_leproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Filter.Tendsto.inseparable_iff_uniformityproof · cited by 1
- eq_of_clusterPt_uniformityproof · cited by 0