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Dimension theory and superpositions of continuous functions

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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} = 1/4i are four functions inC(X), then there exists a functionf inC(X) which cannot be represented in the form:

$$f(x) = \sum\limits_{i = 1}^4 {g_\iota (\varphi _i (x))} $$

, with

$$g_\iota \in C(R)$$

.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    J. Sternfeld

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  1. J. Sternfeld
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Sternfeld, J. Dimension theory and superpositions of continuous functions. Israel J. Math. 20, 300–320 (1975). https://doi.org/10.1007/BF02760335

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  • DOI: https://doi.org/10.1007/BF02760335

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