Theorems · Theorem · Lie groups
AddGroupFilterBasis.nhds_zero_hasBasis
∀ {G : Type u} [inst : AddGroup G] (B : AddGroupFilterBasis G), (nhds 0).HasBasis (fun V => V ∈ B) id- Defined in
- Mathlib.Topology.Algebra.FilterBasis
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- Setstatement and proof · cited by 53,352
- Filterproof · cited by 8,121
- nhdsstatement · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- Filter.HasBasisstatement and proof · cited by 604
- AddGroupFilterBasis.toFilterBasisproof · cited by 32
- AddGroupFilterBasisstatement and proof · cited by 27
- FilterBasis.hasBasisproof · cited by 10
- AddGroupFilterBasis.topologystatement · cited by 7
- AddGroupFilterBasis.nhds_zero_eqproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.hasBasis_nhds_zero_adicproof · cited by 6
- WithSeminorms.hasBasisproof · cited by 5
- RingSubgroupsBasis.hasBasis_nhds_zeroproof · cited by 3
- AddGroupFilterBasis.cauchy_iffproof · cited by 2
- AddGroupFilterBasis.mem_nhds_zeroproof · cited by 1
- SubmodulesBasis.nonarchimedeanproof · cited by 0