Theorems · Theorem · Lie groups
AddGroupFilterBasis.nhds_zero_eq
∀ {G : Type u} [inst : AddGroup G] (B : AddGroupFilterBasis G), nhds 0 = B.filter- Defined in
- Mathlib.Topology.Algebra.FilterBasis
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 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.
Cites11
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
- AddGroupstatement and proof · cited by 4,410
- zero_addproof · cited by 2,366
- Filter.mapproof · cited by 819
- AddGroupFilterBasis.toFilterBasisstatement and proof · cited by 32
- AddGroupFilterBasisstatement and proof · cited by 27
- Filter.map_idproof · cited by 22
- FilterBasis.filterstatement and proof · cited by 19
- AddGroupFilterBasis.topologystatement · cited by 7
- AddGroupFilterBasis.nhds_eqproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfproof · cited by 8
- AddGroupFilterBasis.nhds_zero_hasBasisproof · cited by 6
- SeminormFamily.withSeminorms_of_nhdsproof · cited by 3
- AddGroupFilterBasis.t2Space_iffproof · cited by 1