Region-Based Borsuk-Ulam Theorem
James Francis Peters, Arturo Tozzi · arXiv (Cornell University) · 2016
This paper introduces a region-based extension of the Borsuk-Ulam Theorem (denoted by reBUT). A region is a subset of a surface on a finite-dimensional $n$-sphere. In topology, an $n$-sphere is a generalization of the circle. For a continuous function on an $n$-sphere into $n$-dimensional Euclidean space, there exists a pair of antipodal n-sphere regions with matching descriptions that map into Euclidean space $\mathbb{R}^n$. Applications of reBUT are given in the evaluation of brain activity and quantum entanglement