The Grünhage game and the continuity of $K_h C$ -functions on horizontals
1 Institute of Mathematics, University of Silesia in Katowice, Katowice, 40-007, Poland
2 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords:
the Grünhage game, $K_h C$ -functions
Abstract
It is obtained that the discontinuity point set of any $K_h C$ -function defined on the product of a Baire space and a $W$-space and ranged in a metrizabble space is meager on each horizontal. Besides, we prove the same result for function defined on the product of an $α$-favorable space and a $w$-space.
References
[1] Mirmostofaee A. K. Point of joint continuity of separately continuous mappings // (to appear)
[2] Gruenhage G. Covering properties on $X^2$\ $Δ, W$-sets and compact subsets of $\sum$ -products.// Topology Appl. - 1984. - 17 . - P.287-304.
[3] Saint-Raymond J. Jeux topologiques et espaces de Namioka // Proc. Amer. Math. Soc. - 1984. - 87, N4. - P.409-504.
Cite
- ACS Style
- Maslyuchenko, O.V. The Grünhage game and the continuity of $K_h C$ -functions on horizontals. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Maslyuchenko OV. The Grünhage game and the continuity of $K_h C$ -functions on horizontals. Bukovinian Mathematical Journal. 2018; 1(485).
- Chicago/Turabian Style
- Oleksandr Volodymyrovych Maslyuchenko. 2018. "The Grünhage game and the continuity of $K_h C$ -functions on horizontals". Bukovinian Mathematical Journal. 1 no. 485.
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