  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
$\mathbb{R}^n$. Each region $M$ of a string-covered $n$-sphere is a worldsheet
(denoted by $\mbox{wsh}M$). For a strongly proximal continuous mapping from a
worldsheet-covered $n$-sphere to $\mathbb{R}^n$, strongly near antipodal
worldsheets map into the same region in $\mathbb{R}^n$. An application of
strBUT is given in terms of the evaluation of Electroencephalography (EEG)
patterns.
