Extension of the Borsuk theorem on non-embeddability of spheres

Abstract:

It is proved by elementary techniques that the suspension $\sum M$ of a closed $n$-dimensional manifold $M$, $n\ge 1$, does not embed in a product of $n+1$ curves. Thus we get in particular an elementary proof of a far-reaching generalization of the Borsuk theorem on non-embeddability of the sphere $\mathbb {S}^{n+1}$ in a product of $n+1$ curves. The ultimate results are even more general; they complement and extend some principal results of Koyama, Krasinkiewicz, and Spież.