Theorems · Theorem · Lie groups
closure_subset_add_self_of_mem_nhds_zero
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {U : Set G},
U ∈ nhds 0 → closure U ⊆ U + U- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Set.preimageproof · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- closurestatement and proof · cited by 1,254
- sub_selfproof · cited by 996
- sub_add_cancelproof · cited by 344
- Set.addstatement · cited by 338
- continuousAt_constproof · cited by 59
Cited by2
Results whose statement or proof uses this declaration.
- exists_nhds_hasAntitoneBasis_absConvex_open_add_closure_subsetproof · cited by 0
- nhds_hasBasis_absConvex_closedproof · cited by 0