Theorems · Theorem · Lie groups

ContRepresentation.mem_invariants

∀ {R : Type u_1} {G : Type u_2} {V : Type u_3} [inst : Monoid G] [inst_1 : Ring R] [inst_2 : AddCommGroup V]
  [inst_3 : TopologicalSpace V] [inst_4 : IsTopologicalAddGroup V] [inst_5 : Module R V] {π : ContRepresentation R G V}
  (v : V), v ∈ π.invariants ↔ ∀ (g : G), (π g) v = v

Defined in

Mathlib.RepresentationTheory.Continuous.Basic

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidRingAddCommGroupTopologicalSpaceIsTopologicalAddGroupModule