Two large subsets of a functional space (Q1078684)
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scientific article; zbMATH DE number 3962014
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two large subsets of a functional space |
scientific article; zbMATH DE number 3962014 |
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Two large subsets of a functional space (English)
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1985
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Let P be the Banach space of bounded derivatives f on [0,1] with \(f(x)=0\) for x from a dense subset of [0,1]. Let \(D_ 0\subset P\) consist of functions which are unsigned on every interval and \(D_ 1\subset P\) of functions which are nonzero a.e. in [0,1]. The author proves that \(D_ 0\) and \(D_ 1\) are dense \(G_{\delta}\)-subsets of P with the empty interior.
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Banach space of bounded derivatives
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dense \(G_{\delta }\)-subsets
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