Functions with diagonal of finite Baire class (in Ukrainian) |
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| Author |
Chernivtsi State University
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| Abstract |
It is shown that for a~topological space with normal square and $G_{\delta}$ diagonal and for any Baire $m+1$ class function there exists a continuous with respect to the first variable and Baire $m$ class with respect to the second variable function which is the $m$-th limit of separately continuous functions and coincides with the given function on the diagonal.
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| Keywords |
topological spaces with normal square, Baire class functions, separately continuous functions, diagonal of a function, limits of separately continuous functions, descriptive set theory
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| DOI |
doi:10.30970/ms.14.1.23-28
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Reference |
1. Baire R. Sur les fonctions de variables réelles // Annali di mat. pura ed. appl., ser. 3. – 1899. – V.3. – P.1–123.
2. Lebesgue H. Sur les fonctions représentables analytiquement // Journ. de Math., ser. 2 – 1905. – T.1. – P.139–216. 3. Hahn H. Reelle Funktionen. 1. Teil. Punktfunktionen. — Leipzig: Academische Verlagsgesellschaft M.B.H., 1932. – 416 S. 4. Энгелькинг Р. Общая топология. – Москва: Мир, 1986. – 752 с. |
| Pages |
23-28
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| Volume |
14
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| Issue |
1
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| Year |
2000
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |