Extension of the Borsuk Theorem on Non-Embeddability of Spheres

TL;DR

This paper generalizes Borsuk's theorem by proving that the suspension of any closed n-dimensional manifold cannot embed in a product of n+1 curves, extending non-embeddability results to broader settings.

Contribution

It extends Borsuk's non-embeddability theorem to a more general class of manifolds and embedding spaces.

Findings

Suspension of closed n-manifolds does not embed in a product of n+1 curves.

The result is generalized to a broader setting beyond spheres.

Provides new insights into topological embedding limitations.

Abstract

It is proved that the suspension of a closed n-dimensional manifold M, $n\ge1$, does not embed in a product of n+1 curves. In fact, the ultimate result will be proved in a much more general setting. This is a far-reaching generalization the Borsuk theorem on non-embeddability of the (n+1)-dimensional sphere in a product of n+1 curves.