On Borsuk's non-retract theorem final version

Abstract

The classical Borsuk's non-retract theorem asserts that a unit sphere in ${\mathbb{R}}^n$ is not a continuous retract of the unit closed ball. We will show that such a unit sphere is a piecewise continuous retract of the unit closed ball.

4 pages. arXiv admin note: substantial text overlap with arXiv:2312.03765