About Baire property of space of separately continuous functions
We propose three methods for proving that locally convexspace $S = CC [0,1] ^ 2$ of separately continuous functions $f:[0,1] ^2 \rightarrow \mathbb {R}$ on the square $[ 0,1] ^ 2$ withtopology of layer-wise uniform convergence is the set of the firstcategory, therefore, is not Baire space. The metho...
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| Date: | 2015 |
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| Keywords: | keywords |
| Main Authors: | , , , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2015
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/167 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | We propose three methods for proving that locally convexspace $S = CC [0,1] ^ 2$ of separately continuous functions $f:[0,1] ^2 \rightarrow \mathbb {R}$ on the square $[ 0,1] ^ 2$ withtopology of layer-wise uniform convergence is the set of the firstcategory, therefore, is not Baire space. The methods of$\varepsilon$-nets, function of calculation or topological gameswere used in this research. These approaches were generalized onspaces $CC (X \times Y)$ of separately continuous functions $f: X\times Y \rightarrow \mathbb {R} $, which were topologizedrespectively. |
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