On embeddings of topological groups II

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