On the set \(B^{**}_1\) in the space \(B_1\) of functions (Q2774519)
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scientific article; zbMATH DE number 1713826
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the set \(B^{**}_1\) in the space \(B_1\) of functions |
scientific article; zbMATH DE number 1713826 |
Statements
28 February 2002
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Baire one two stars function
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Baire one function
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Darboux function
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porosity
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metric of uniform convergence
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road
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quasi-continuous function
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0.8780218
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0.8748116
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On the set \(B^{**}_1\) in the space \(B_1\) of functions (English)
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Let \(B_1^{**}\) be a family of all Darboux functions such that for each of them its restriction to the set of all its discontinuity points is a continuous function. In this paper it is shown that the class of all continuous functions is a porous set at each point of \(B_1^{**}\) and the class \(B_1^{**}\) is a porous set at each point of \(B_1\), and for an arbitrary real function defined on the closure of \(B_1^{**}\) there exists its Darboux and quasi-continuous extension to the whole space \(B_1\).
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