Theorems · Definition · Lie groups

OpenSubgroup.comap

{G : Type u_1} →
  [inst : Group G] →
    [inst_1 : TopologicalSpace G] →
      {N : Type u_2} →
        [inst_2 : Group N] →
          [inst_3 : TopologicalSpace N] → (f : G →* N) → Continuous ⇑f → OpenSubgroup N → OpenSubgroup G

The preimage of an OpenSubgroup along a continuous Monoid homomorphism is an OpenSubgroup.

Defined in: Mathlib.Topology.Algebra.OpenSubgroup
Cited by: 4 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext
Assumes: Group TopologicalSpace Group TopologicalSpace

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

Cites8

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

DFunLike.coestatement and proof · cited by 62,936
TopologicalSpacestatement and proof · cited by 24,529
Groupstatement and proof · cited by 6,238
MonoidHomstatement and proof · cited by 3,629
Continuousstatement and proof · cited by 2,592
Subgroup.comapproof · cited by 154
OpenSubgroupstatement and proof · cited by 47
OpenSubgroup.toSubgroupproof · cited by 34

Cited by4

Results whose statement or proof uses this declaration.

OpenSubgroup.toSubgroup_comapstatement · cited by 0
OpenSubgroup.mem_comapstatement · cited by 0
OpenSubgroup.comap_comapstatement · cited by 0
OpenSubgroup.coe_comapstatement · cited by 0