Mathlib Map

Theorems · Definition · Lie groups

AddSubgroup.topologicalClosure

{G : Type w} →
  [inst : TopologicalSpace G] → [inst_1 : AddGroup G] → [IsTopologicalAddGroup G] → AddSubgroup G → AddSubgroup G

The (topological-space) closure of an additive subgroup of an additive topological group is itself an additive subgroup.

Defined in
Mathlib.Topology.Algebra.Group.Basic
Cited by
16 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddGroupIsTopologicalAddGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subring.topologicalClosure · cited by 4Subring.topologicalClosureNonUnitalSubring.topologicalClosure · cited by 4NonUnitalSubring.topologi…compl_add_closure_zero_eq · cited by 1compl_add_closure_zero_eqAddSubgroup.coe_topologicalClosure_bot · cited by 1AddSubgroup.coe_topologic…mapClusterPt_atTop_nsmul_iff_mem_topologicalClosure_zmultiples · cited by 1mapClusterPt_atTop_nsmul_…AddSubgroup.topologicalClosure_coe · cited by 1AddSubgroup.topologicalCl…controlled_closure_of_complete · cited by 1controlled_closure_of_com…mapClusterPt_neg_atTop_nsmul · cited by 0mapClusterPt_neg_atTop_ns…AddSubgroup.norm_normedMk · cited by 0AddSubgroup.norm_normedMkAddSubgroup.le_topologicalClosure · cited by 0AddSubgroup.le_topologica…AddSubgroup.norm_trivial_quotient_mk · cited by 0AddSubgroup.norm_trivial_…MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure · cited by 0Lp.boundedContinuousFunct…controlled_closure_range_of_complete · cited by 0controlled_closure_range_…AddSubgroup.is_normal_topologicalClosure · cited by 0AddSubgroup.is_normal_top…AddSubgroup.topologicalClosure_mono · cited by 0AddSubgroup.topologicalCl…TopologicalSpace · cited by 24529TopologicalSpaceSetLike.coe · cited by 8199SetLike.coeAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupIsTopologicalAddGroup · cited by 1394IsTopologicalAddGroupclosure · cited by 1254closureAddSubmonoid · cited by 1178AddSubmonoidAddSubgroup.toAddSubmonoid · cited by 91AddSubgroup.toAddSubmonoidAddSubmonoid.topologicalClosure · cited by 6AddSubmonoid.topologicalC…AddSubgroup.topologicalClosureCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.