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Diadic Baire space and continuity of weakly quasi-continuous maps(in Ukrainian) |
| Author |
O. V. Maslyuchenko
ovmasl@gmail.com
×åðí³âåöüêèé íàö³îíàëüíèé óí³âåðñèòåò ³ì. Þ. Ôåäüêîâè÷à
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| 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 |
| Reference |
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P. 559–564.
4. Maslyuchenko O.V. Joint continuity of KC-functions// Mat. Stud. – 2002. – V.17, ¹1. – P. 75–80. (in
Ukrainian)
5. Saint-Raymond J. Jeux topologiques et espaces de Namioka// Proc. Amer. Math. Soc. – 1984. – V.87, ¹4.
– P. 409–504.
6. Ýíãåëüêèíã Ð. Îáùàÿ òîïîëîãèÿ. - Ìîñêâà: Ìèð, 1986. - 752ñ.
7. Àðõàíãåëüñêèé À.Â. Òîïîëîãè÷åñêèå ïðîñòðàíñòâà ôóíêöèé. - Ì.:
Èçä. Ìîñêîâñêîãî óí-òà, 1989. - 222ñ.
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| Pages |
107-112 |
| Volume |
36 |
| Issue |
1 |
| Year |
2011 |
Journal |
Matematychni Studii |
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