Theorems · Theorem · Lie groups
AddGroupFilterBasis.nhds_eq
∀ {G : Type u} [inst : AddGroup G] (B : AddGroupFilterBasis G) {x₀ : G}, nhds x₀ = B.N x₀- Defined in
- Mathlib.Topology.Algebra.FilterBasis
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- Set.imageproof · cited by 5,609
- nhdsstatement · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- add_zeroproof · cited by 2,707
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Filter.HasBasis.mapproof · cited by 51
- vadd_vaddproof · cited by 40
- Filter.image_mem_mapproof · cited by 39
- AddGroupFilterBasis.toFilterBasisproof · cited by 32
Cited by3
Results whose statement or proof uses this declaration.
- AddGroupFilterBasis.nhds_zero_eqproof · cited by 4
- AddGroupFilterBasis.nhds_hasBasisproof · cited by 2
- WithSeminorms.toLocallyConvexSpaceproof · cited by 1