Let τ and γ be infinite cardinal numbers with τ⩽γ. A subset Y of a space X is called Cτ-compact if f[Y] is compact for every continuous function f:X→Rτ. We prove that every Cτ-compact dense subspace of a product of γ non-trivial compact spaces each of them of weight ⩽τ is 2τ-resolvable. In particular, every pseudocompact dense subspace of a product of non-trivial metrizable compact spaces is c-resolvable. As a consequence of this fact we obtain that there is no σ-independent maximal independent family. Also, we present a consistent example, relative to the existence of a measurable cardinal, of a dense pseudocompact subspace of {0,1}2λ, with λ=2ω1, which is not maximally resolvable. Moreover, we improve a result by W. Hu (2006) [17] by showing that if maximal θ-independent families do not exist, then every dense subset of □θ{0,1}γ is ω-resolvable for a regular cardinal number θ with ω1⩽θ⩽γ. Finally, if there are no maximal independent families on κ of cardinality γ, then every Baire dense subset of {0,1}γ of cardinality ⩽κ and every Baire dense subset of [0,1]γ of cardinality ⩽κ are ω-resolvable.