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http://hdl.handle.net/10662/13439
Title: | Convex sets without diametral pairs |
Authors: | Veselý, Libor |
Keywords: | Diametral pair;Bounded closed convex set;Hausdorff metric;Par diametral;Conjunto convexo cerrado acotado;Métrica de Hausdorff |
Issue Date: | 2009 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | Let X be an infinite dimensional normed linear space. It is not difficult to see that arbitrarily near (in the Hausdorrff metric) to the unit ball of X there exists a nonempty closed convex set whose diameter is not attained. We show that such sets are dense in the metric space of all nonempty bounded closed convex subsets of X if and only if either X is not a reflexive Banach space or X is a reflexive Banach space in which every weakly closed set contained in the unit sphere Sx has empty relative interior in Sx. |
URI: | http://hdl.handle.net/10662/13439 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 24, nº 3 (2009) |
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0213-8743_24_3_271.pdf | 170,07 kB | Adobe PDF | View/Open |
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