Theorems · Theorem · general topology
Metric.disjoint_nhds_cobounded
∀ {α : Type u} [inst : PseudoMetricSpace α] (x : α), Disjoint (nhds x) (Bornology.cobounded α)- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 120 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Disjointstatement · cited by 2,201
- PseudoMetricSpacestatement and proof · cited by 1,550
- Bornology.coboundedstatement · cited by 162
- one_posproof · cited by 102
- Metric.ball_mem_nhdsproof · cited by 64
- disjoint_compl_rightproof · cited by 47
- Metric.isBounded_ballproof · cited by 15
- Filter.disjoint_of_disjoint_of_memproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- NormedField.continuousAt_zpowproof · cited by 3
- Real.not_continuousAt_inv_log_oneproof · cited by 2
- Real.not_continuousAt_log_log_oneproof · cited by 2
- Metric.disjoint_nhdsSet_coboundedproof · cited by 1
- Metric.exists_isBounded_image_of_tendstoproof · cited by 1
- Real.not_continuousAt_log_log_zeroproof · cited by 1
- Metric.disjoint_cobounded_nhdsproof · cited by 1