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Points of joint continuity of separately continuous mappings

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Abstract

Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $f:X \times Y \to \mathbb{R}$ be a separately continuous mapping. For each $y \in Y$, we define a game $G(Y, \{ y \})$ between players $O$ and $P$, to show that if in this game either $O$ player has a winning strategy or $X$ is $\alpha$-favorable and $P$ player does not have a winning strategy, then for each countable subset $E$ of $Y$, there exists a dense $G_\delta$ subset $D$ of $X$ such that $f$ is jointly continuous on $D \times E$.


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Article Information

TitlePoints of joint continuity of separately continuous mappings
SourceMethods Funct. Anal. Topology, Vol. 15 (2009), no. 4, 356-360
MathSciNet MR2603833
CopyrightThe Author(s) 2009 (CC BY-SA)

Authors Information

Alireza Kamel Mirmostafaee
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran; Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran 


Citation Example

Alireza Kamel Mirmostafaee, Points of joint continuity of separately continuous mappings, Methods Funct. Anal. Topology 15 (2009), no. 4, 356-360.


BibTex

@article {MFAT491,
    AUTHOR = {Mirmostafaee, Alireza Kamel},
     TITLE = {Points of joint continuity of separately continuous mappings},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {356-360},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=491},
}


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