Domination in products

In this note we continue to study the cardinal invariants dm and sdm introduced by the author in [7]. We prove that if K   is a compact subspace of Cp(Y)Cp(Y) for some space Y   such that dm(Y)≤κdm(Y)≤κ then K is strongly κ-monolithic. Also we show how GCH   implies that if sdm(Cp(X))≤ωsdm(Cp(X))≤ω for some hereditarily normal space X   of character at most cc then every infinite compact subset of X is countable. Finally we show that for every cardinal κ there is a metric space of weight at most κ   that condenses onto Σ(2κ)Σ(2κ).