Diadic Baire space and continuity of weakly quasi-continuous maps(in Ukrainian)

Author O. V. Maslyuchenko
ovmasl@gmail.com
Yuriy Fedkovych Chernivtsi National University

Abstract We introduce some diadic analogue of the Choquet game and a class of diadic Baire spaces which is a subclass of Baire spaces and is wider then the class Choquet spaces. We prove that for any diadic Baire space $X$, a Banach space $Y$, a countable Asplund$^*$ norming set $E\subseteq Y^*$ and for every map $\varphi\colon X\to Y$, such that $z\varphi$ is quasi-continuous for any $z\in E$, the discontinuity point set $C(\varphi)$ is residual.
Keywords Choquet game; diadic Baire space
DOI
doi:10.30970/ms.36.1.107-112
Reference 1. Baire R. Sur les fonctions de variables reelles// Annal Mat. Pura Appl. – 1899. – V.3, №3. – P. 1–123.

2. Namioka I. Separate continuity and joint continuity// Pacif. J. Math. – 1974. – V.51, №2. – P. 515–531.

3. Stegall Ch. Generalization of a theorem of Namioka// Proc. Amer. Math. Soc. – 1988. – V.102, №3. – P. 559–564.

4. Maslyuchenko O.V. Joint continuity of KC-functions// Mat. Stud. – 2002. – V.17, №1. – P. 75–80. (in Ukrainian)

5. Saint-Raymond J. Jeux topologiques et espaces de Namioka// Proc. Amer. Math. Soc. – 1984. – V.87, №4. – P. 409–504.

6. Энгелькинг Р. Общая топология. - Москва: Мир, 1986. - 752с.

7. Архангельский А.В. Топологические пространства функций. - М.: Изд. Московского ун-та, 1989. - 222с.

Pages 107-112
Volume 36
Issue 1
Year 2011
Journal Matematychni Studii
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