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<dc:title lang="ca-ES">$C$-nearest points and the drop property</dc:title>
<dc:creator>Maâden, Abdelhakim</dc:creator>
<dc:description lang="ca-ES">For a closed convex set $C$ with non-empty interior, we define the $C$-nearest distance from $x$ to a closed set $F$. We show that, if there exists in the Banach space $X$ a closed convex set with non-empty interior satisfying the drop property, then for all closed subset $F$ of $X$, there exists a dense $G_\delta$ subset $\Gamma$ of $X\setminus \{x; \rho(F, x) = 0\}$ such that every $x\in\Gamma$ has a $C$-nearest point in $F$. We also prove that every smooth (unbounded) convex set with the drop property has the smooth drop property.</dc:description>
<dc:publisher lang="0">Universitat de Barcelona</dc:publisher>
<dc:date>1995</dc:date>
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<dc:identifier>https://www.raco.cat/index.php/CollectaneaMathematica/article/view/56316</dc:identifier>
<dc:identifier>2038-4815</dc:identifier>
<dc:source lang="ca-ES">Collectanea Mathematica; 1995: Vol.: 46 Núm.: 3; p. 289-301</dc:source>
<dc:source lang="0">0010-0757</dc:source>
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<dc:rights>Aquesta revista ofereix el text complet de tots els seus articles, excepte els dels cinc darrers anys, que s'aniran alliberant periòdicament fins el 2010. A partir del 2011 requereix subscripció. Podeu accedir-hi aquí. L'accés als articles a text complet inclosos a RACO és gratuït, però els actes de reproducció, distribució, comunicació pública o transformació total o parcial estan subjectes a les condicions d'ús de cada revista i poden requerir el consentiment exprés i escrit dels autors i/o institucions editores.</dc:rights>
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