On closed sets with convex projections in Hilbert space

S.T. Barov, J.J. Dijkstra

Research output: Contribution to JournalArticleAcademicpeer-review


Let k be a fixed natural number. We show that if C is a closed and nonconvex set in Hilbert space such that the closures of the projections onto all k-hyperplanes (planes with codimension k) are convex and proper, then C must contain a closed copy of Hilbert space. In order to prove this result we introduce for convex closed sets B the set ε
Original languageEnglish
Pages (from-to)17-33
JournalFundamenta Mathematicae
Publication statusPublished - 2007

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