Definition 2

A representation $\varrho$ of G in a topological K-vector space E is said to be irreducible if $\{0\}$ is not dense in E and if the only subrepresentations of $\varrho$ are $\varrho$ and the representation in the closure of $\{0\}$.

If $\varrho$ is an irreducible representation of G in a separated topological vector space E, then every nonzero element of E is a cyclic vector for $\varrho$.