Theorems · Theorem · general topology
vadd_mem_nhds_self
∀ {G : Type u_4} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [ContinuousConstVAdd G G] {g : G} {s : Set G},
g +ᵥ s ∈ nhds g ↔ s ∈ nhds 0- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- Set.vaddSetstatement · cited by 403
- neg_add_cancelproof · cited by 256
- ContinuousConstVAddstatement and proof · cited by 97
- neg_vadd_vaddproof · cited by 34
- vadd_mem_nhds_vadd_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- FiniteDimensional.of_totallyBounded_nhdsproof · cited by 1
- vadd_singleton_mem_nhds_of_sigmaCompactproof · cited by 1