Dense families of continuous selections

E. Michael

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An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_{X} (e)$ from e to X has fixed cardinality n+1 ( $n \subseteq ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_{X} (e)$ from e to X where X is a compact subset of .