Continuous piecewise-linear functions from R/sup n/ to R/sup m/ are analyzed in terms of the dimensions of their domain space and of degenerate kth-order intersections of region boundaries. The theory developed demonstrates how these two quantities are connected. Moreover, the exact number of independent parameters is demonstrated for boundary configurations containing degenerate intersections of arbitrary orders.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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