String-Based Borsuk-Ulam Theorem James F Peters A Tozzi arXiv:1606.04031v1 This paper introduces a string-based extension of the Borsuk-Ulam Theorem (denoted by strBUT). A string is a region with zero width and either bounded or unbounded length on the surface of an n -sphere or a region of a normed linear space. In this work, an n -sphere surface is covered by a collection of strings. For a strongly proximal continuous function on an n -sphere into n-dimensional Euclidean space, there exists a pair of antipodal n-sphere strings with matching descriptions that map into Euclidean space. Each region M of a string-covered n-sphere is a worldsheet (denoted by wshM). For a strongly proximal continuous mapping from a worldsheet-covered n -sphere to R n, strongly near antipodal worldsheets map into the same region in Rn. An application of strBUT is given in terms of the evaluation of Electroencephalography (EEG) patterns.