On the sums of functions satisfying the condition \((s_ 1)\). (Q595845)
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scientific article; zbMATH DE number 2084018
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sums of functions satisfying the condition \((s_ 1)\). |
scientific article; zbMATH DE number 2084018 |
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On the sums of functions satisfying the condition \((s_ 1)\). (English)
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6 August 2004
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In [Real Anal. Exch. 24, No. 1, 171--183 (1998; Zbl 0940.26003)], the author defined when a function \(f:\mathbb R\to\mathbb R\) satisfies the condition (\(s_1\)), respectively (\(s_2\)). In the present paper he proves the following result: If a function \(f\) is a sum of functions \(g\) and \(h\) having property (\(s_1\)), or if \(f\) has property (\(s_2\)), then there exist Darboux functions \(\phi\) and \(\psi\) with the property (\(s_1\)) such that \(f=\phi+\psi\).
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density topology
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condition \((s_1)\)
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condition \((s_2)\)
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Darboux functions
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generalized continuity
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