About Baire property of space of separately continuous functions

• Date: 2015
• Main Authors: Voloshyn, G. A., Maslyuchenko, V. K., Maslyuchenko, A. V., Волошин, Г. А., Маслюченко, В. К., А. В., Маслюченко, О. В.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2015
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/167
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

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...