This is an announcement for the paper "On \sigma-convex subsets in spaces of scatteredly continuous functions" by Taras Banakh, Bogdan Bokalo, and Nadiya Kolos.
Abstract: We prove that for any topological space $X$ of countable tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$ of scatteredly continuous real-valued functions on $X$ has network weight $nw(\F)\le nw(X)$. This implies that for a metrizable separable space $X$, each compact convex subset in the function space $SC_p(X)$ is metrizable. Another corollary says that two Tychonoff spaces $X,Y$ with countable tightness and topologically isomorphic linear topological spaces $SC_p(X)$ and $SC_p(Y)$ have the same network weight $nw(X)=nw(Y)$. Also we prove that each zero-dimensional separable Rosenthal compact space is homeomorphic to a compact subset of the function space $SC_p(\omega^\omega)$ over the space $\omega^\omega$ of irrationals.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 46A55, 46E99, 54C35
Remarks: 6 pages
Submitted from: tbanakh@yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2438
or