# Region-Based Borsuk-Ulam Theorem

# Region-Based Borsuk-Ulam Theorem

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-dimensionaln n-sphere. In topology, an nn -sphere is a generalization of the circle. For a continuous function on an nn -sphere into nn -dimensional Euclidean space, there exists a pair of antipodal n-sphere regions with matching descriptions that map into Euclidean space R^nRn . Applications of reBUT are given in the evaluation of brain activity and quantum entanglement

Comments: | 15 pages, 7 figures |

Subjects: | General Topology (math.GN) |

MSC classes: | 54E05, 37J05 |

Cite as: | arXiv:1605.02987 [math.GN] |

(or arXiv:1605.02987v1 [math.GN] for this version) |