Theorems · Theorem · general topology
WithZeroTopology.nhds_zero
∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀], nhds 0 = ⨅ γ, ⨅ (_ : γ ≠ 0), Filter.principal (Set.Iio γ)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- iInfstatement and proof · cited by 1,690
- Set.Iiostatement and proof · cited by 1,166
- Filter.principalstatement and proof · cited by 740
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Function.update_selfproof · cited by 201
- WithZeroTopology.topologicalSpacestatement · cited by 27
- WithZeroTopology.nhds_eq_updateproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- WithZeroTopology.hasBasis_nhds_zeroproof · cited by 4
- WithZeroTopology.tendsto_zeroproof · cited by 2