Extensions of functions on product spaces

Let X be a topological space and A its subspace. The following problem posed by Przymusiński in 1983 remains open: for a nondiscrete metric space Y is it true that A × Y is C∗ -embedded in X × Y iff A × Y is C-embedded in X × Y? In this paper first we prove that this problem is affirmative in case of nondiscrete metrizable Y with Y = Y2, which contains therefore the cases that Y is the Baire zero-dimensional metric space B(κ), Hilbert space Rℵ0 and J(κ)ℵ0, where J(κ) is a hedgehog of κ spines. Secondly, we discuss some results of equivalence between C∗-embedding (or C-embedding) and P-embedding of A × Y in X × Y in case of Y being a paracompact Σ- or σ-space.