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 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 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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     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 },
     year = {2005},
     volume = {30},
     doi = {10.2298/BMAT0530029T},
     zbl = {1144.46009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530029T/}
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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

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