Theorems · Definition · Lie groups
AddSubgroup.topologicalClosure
{G : Type w} →
[inst : TopologicalSpace G] → [inst_1 : AddGroup G] → [IsTopologicalAddGroup G] → AddSubgroup G → AddSubgroup GThe (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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- closureproof · cited by 1,254
- AddSubmonoidproof · cited by 1,178
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddSubmonoid.topologicalClosureproof · cited by 6
Cited by19
Results whose statement or proof uses this declaration.
- Subring.topologicalClosureproof · cited by 4
- NonUnitalSubring.topologicalClosureproof · cited by 4
- compl_add_closure_zero_eqproof · cited by 1
- AddSubgroup.coe_topologicalClosure_botstatement · cited by 1
- mapClusterPt_atTop_nsmul_iff_mem_topologicalClosure_zmultiplesstatement · cited by 1
- AddSubgroup.topologicalClosure_coestatement · cited by 1
- controlled_closure_of_completestatement and proof · cited by 1
- mapClusterPt_neg_atTop_nsmulproof · cited by 0
- AddSubgroup.norm_normedMkstatement and proof · cited by 0
- AddSubgroup.le_topologicalClosurestatement · cited by 0
- AddSubgroup.norm_trivial_quotient_mkstatement and proof · cited by 0
- MeasureTheory.Lp.boundedContinuousFunction_topologicalClosurestatement · cited by 0