The compact Z-set property in convex sets
A metric space X has the compact Z-set property if all compacta of X are Z-sets (a closed subset A of X is a Z-set if any map of any finite- dimensional cell into X is arbitrary closely approximable by a map into \(X\setminus A)\). Let C be an infinite-dimensional, \(\sigma\)-fd-compact (i.e. countable union of finite-dimensional compacta), convex subset of a complete metric linear space. The main result says that C has the compact Z-set property (and hence C is a \(\sigma\)-Z-set in \(\bar C)\). There are given three conditions (e.g., \(\bar C\) not locally compact) each implying that C is homeomorphic to \(\ell^ f_ 2\).
scientific article; zbMATH DE number 3955873
scientific article