Theorems · Theorem · general topology
WithZeroTopology.nhds_of_ne_zero
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {γ : Γ₀}, γ ≠ 0 → nhds γ = pure γThe neighbourhood filter of a nonzero element consists of all sets containing that element.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- iInfproof · cited by 1,690
- Set.Iioproof · cited by 1,166
- Filter.principalproof · cited by 740
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- WithZeroTopology.topologicalSpacestatement · cited by 27
- nhds_nhdsAdjoint_of_neproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- WithZeroTopology.tendsto_of_ne_zeroproof · cited by 5
- WithZeroTopology.hasBasis_nhds_of_ne_zeroproof · cited by 2
- WithZeroTopology.isOpen_iffproof · cited by 1
- WithZeroTopology.singleton_mem_nhds_of_ne_zeroproof · cited by 1
- WithZeroTopology.Iio_mem_nhdsproof · cited by 1
- WithZeroTopology.nhds_coe_unitsproof · cited by 0
- WithZeroTopology.orderClosedTopologyproof · cited by 0
- WithZeroTopology.singleton_mem_nhds_of_unitsproof · cited by 0