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Theorems · Definition · Lie groups

OpenSubgroup.prod

{G : Type u_1} →
  [inst : Group G] →
    [inst_1 : TopologicalSpace G] →
      {H : Type u_2} →
        [inst_2 : Group H] → [inst_3 : TopologicalSpace H] → OpenSubgroup G → OpenSubgroup H → OpenSubgroup (G × H)

The product of two open subgroups as an open subgroup of the product group.

Defined in
Mathlib.Topology.Algebra.OpenSubgroup
Cited by
2 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupTopologicalSpaceGroupTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OpenSubgroup.coe_prod · cited by 0OpenSubgroup.coe_prodOpenSubgroup.toSubgroup_prod · cited by 0OpenSubgroup.toSubgroup_p…TopologicalSpace · cited by 24529TopologicalSpaceGroup · cited by 6238GroupOpenSubgroup · cited by 47OpenSubgroupSubgroup.prod · cited by 35Subgroup.prodOpenSubgroup.toSubgroup · cited by 34OpenSubgroup.toSubgroupOpenSubgroup.prodCITED BYCITES

Cites5

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Cited by2

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