Geodesic
On Typical Compact Convex Sets in Hilbert Spaces
Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 255-268

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Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.
Keywords: Compact Convex Set, Metric Antiprojection, Multivalued Locus, Baire Category 
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     author = {De Blasi, F.},
     title = {On {Typical} {Compact} {Convex} {Sets} in {Hilbert} {Spaces}},
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De Blasi, F. On Typical Compact Convex Sets in Hilbert Spaces. Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 255-268. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_3-4_a6/