On dense subsets, convergent sequences and projections of Tychonoff products

We prove (Theorem 3.4) that in ∏α∈2ωIα there is a countable set, that is dense but sequentially closed in ∏α∈2ωIα with the Tychonoff topology and is closed and discrete in ∏α∈2ωIα with the box topology (Theorem 3.4).