Theorems · Theorem · Lie groups

DenseRange.topologicalClosure_map_subgroup

∀ {G : Type w} {H : Type x} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
  [inst_3 : Group H] [inst_4 : TopologicalSpace H] [inst_5 : IsTopologicalGroup H] {f : G →* H},
  Continuous ⇑f →
    DenseRange ⇑f → ∀ {s : Subgroup G}, s.topologicalClosure = ⊤ → (Subgroup.map f s).topologicalClosure = ⊤

Defined in

Mathlib.Topology.Algebra.Group.Basic

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupGroupTopologicalSpaceIsTopologicalGroup