# A characterization of the Hahn property

 Title A characterization of the Hahn property Publication Type Journal Article Year of Publication 2014 Authors Nesterenko, VV Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2014.02.032 Issue 2 Section Mathematics Pagination 32-37 Date Published 2/2014 Language Ukrainian Abstract We prove a new generalization of the Calbrix–Troallic theorem. For a Baire space $X$, a metrizable compact $Y$, and a metric space $Z$, the necessary and sufficient conditions for a mapping $f\colon X\times Y\to Z$, for which a set of points $x$ of $X$ such that $f$ is jointly continuous at each point of the set $\{x\}\times Y$ is residual in $X$, are found. Keywords Calbrix–Troallic theorem, characterization, Hahn property
References:

1. Calbrix J., Troallic J. P. C. r. Acad. Sci. Paris. Sér. A, 1979, 288. 647–648.
2. Maslyuchenko V. K. Mat. metody i fiz.-mekh. polia, 1998, 41, No. 4: 39–45 (in Ukrainian).
3. Maslyuchenko V. K., Nesterenko V. V. Ukr. mat. zhurn., 2000, 52, No. 12: 1711–1714 (in Ukrainian).
4. Maslyuchenko V. K., Nesterenko V. V. Ukr. mat. zhurn., 2010, 62, No. 6: 791-800 (in Ukrainian).
5. Bouziad A., Troallic J. P. Topol. Appl., 2010, 157, No. 18: 2889–2894. https://doi.org/10.1016/j.topol.2010.10.004
6. Nesterenko V. V. Mat. visn. NTSh, 2008, 5: 177– 182 (in Ukrainian).
7. Maslyuchenko V. K., Nesterenko V. V. On a new generalization theorem Kalbri-Troallika. Proceedings of the Ukrainian conference “Modern problems of probability theory and mathematical analysis”, Ivano-Frankivsk, 2013: 65–66 (in Ukrainian).
8. Nesterenko V. V. Characterization of the properties of Ghana. Proceedings of the Ukrainian conference “Modern problems of probability theory and mathematical analysis”, Vorokhta, 2012:. 45–46 (in Ukrainian).