On Typical Compact Convex Sets in Hilbert Spaces

De Blasi, F.. "On Typical Compact Convex Sets in Hilbert Spaces." Serdica Mathematical Journal 23.3-4 (1997): 255-268. <http://eudml.org/doc/11618>.

@article{DeBlasi1997,
abstract = {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.},
author = {De Blasi, F.},
journal = {Serdica Mathematical Journal},
keywords = {Compact Convex Set; Metric Antiprojection; Multivalued Locus; Baire Category; metric antiprojection; Baire category; compact convex set; multivalued locus},
language = {eng},
number = {3-4},
pages = {255-268},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Typical Compact Convex Sets in Hilbert Spaces},
url = {http://eudml.org/doc/11618},
volume = {23},
year = {1997},
}

TY - JOUR
AU - De Blasi, F.
TI - On Typical Compact Convex Sets in Hilbert Spaces
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 3-4
SP - 255
EP - 268
AB - 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.
LA - eng
KW - Compact Convex Set; Metric Antiprojection; Multivalued Locus; Baire Category; metric antiprojection; Baire category; compact convex set; multivalued locus
UR - http://eudml.org/doc/11618
ER -