Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXI, No. 30, pp. 29–45 (2005) 

Representing trees as relatively compact subsets of the first Baire classS. TodorcevicMatematicki Institut, Kneza Mihaila 35, 11001 Beograd, Serbia and Montenegro, email:stevo@mi.sanu.ac.yuAbstract: 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 Frechetdifferentiable norm and its weak topology fails to be $\sigma$fragmented by the norm. Keywords: Baire Class1, Function spaces, Renorming Classification (MSC2000): 46B03, 46B05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 21 Nov 2005. This page was last modified: 20 Jun 2011.
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