  Inspired by the analogous result in the algebraic setting (Theorem 1) we show
(Theorem 2) that the product $M \times \mathbb{R}P^n$ of a closed and
orientable topological manifold $M$ with the $n$-dimensional real projective
space cannot be topologically locally flat embedded into $\mathbb{R}P^{m + n +
1}$ for all even $n > m$.
