Dimension theory and superpositions of continuous functions |
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| Authors: | J. Sternfeld |
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| Affiliation: | 1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
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| Abstract: | The main result of this paper is the following: IfX is a compact two dimensional metric space, and {φ i} i = 1/4 are four functions inC(X), then there exists a functionf inC(X) which cannot be represented in the form: $$f(x) = sumlimits_{i = 1}^4 {g_iota (varphi _i (x))} $$ , with $$g_iota in C(R)$$ . |
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