On embeddings of topological groups II

In the present note, for given cardinals τ and μ, τ ≤ μ , we construct a topological group of character τ and of weight ≤ 2 μ containing topologically all topological groups of character τ and of weight μ. In particular, if τ = ω , then there exists a metrizable group of weight ≤ 2 μ containing topologically all metrizable groups of weight ≤μ.