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Kolmogorov superpositions and Hecht-Nielsen's neural network based on them are dimension reducing. This dimension reduction can be understood in terms of space-filling curves that characterize Kolmogorov's functions, and the subject of this paper is the construction of such a curve. We construct a space-filling curve with Lebesgue measure 1 in the unit square, [0,1] 2 , with approximating...
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