Geodesic
Representing trees as relatively compact subsets of the first Baire class
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We show that there is a scattered compact subset $K$ of the first Baire class, a Baire space $X$ and a separately continuous mapping $f:X\times K\arr{\mbb R}$ which is not continuous on any set of the form $G\times K$, where $G$ is a comeager subset of $X$. We also show that it is possible to have a scattered compact subset $K$ of the first Baire class which does have the Namioka property though its function space ${\mcal C}(K)$ fails to have an equivalent Fréchet-differentiable norm and its weak topology fails to be $\sigma$-fragmented by the norm.
Keywords: Baire Class-1, Function spaces, Renorming 
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     author = {S. Todor\v{c}evi\'c},
     title = {Representing trees as relatively compact subsets of the first {Baire} class},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {29 - 45},
     year = {2005},
     volume = {30},
     number = {1},
     zbl = {1144.46009},
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}
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S. Todorčević. Representing trees as relatively compact subsets of the first Baire class. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005) no. 1. http://geodesic.mathdoc.fr/item/BASS_2005_30_1_a2/