A function f from a countable product X of of Polish
spaces X_{i} into a Polish space
is separately nowhere constant provided it is nowhere constant
on every section of X.
We show that every continuous separately nowhere constant function
is one-to-one on a product of perfect subsets of X_{i}'s.
This result is used to distinguish between
n-cube density notions for different n\leq\omega, where
\omega-cube density is a basic
notion behind the Covering Property Axiom
CPA formulated by Ciesielski and Pawlikowski.
We will also distinguish, for different values of \alpha<\omega_{1},
between the notions of \alpha-prism densities
--- the more refined density notions used also in CPA.

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**Last modified September 12, 2005.**