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), p. 29 .

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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 Fr�chet-differentiable norm and its weak topology fails to be $\sigma$-fragmented by the norm.
DOI : 10.2298/BMAT0530029T
Classification : 46B03 46B05
Keywords: Baire Class-1, Function spaces, Renorming 
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     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 },
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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), p. 29 . doi : 10.2298/BMAT0530029T. http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530029T/

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