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Feb 5, 2014 at 12:07 comment added Igor Belegradek @WlodzimierzHolsztynski, at least I do not see why such a classification is impossible. As I mentioned, all $G_\delta$ (i.e. all completely metrizable) subsets are homeomorphic.
Feb 5, 2014 at 5:36 comment added Włodzimierz Holsztyński Let $B\subset C$ be the centrally symmetric open and closed unit balls in $\ell^2$. Do you mean in particular to classify topologically all sets $X$ such that $B\subseteq X\subseteq C$?
Feb 5, 2014 at 3:42 history asked Igor Belegradek CC BY-SA 3.0