Some Čebyšev sets with dimension d + 1 in hyperspaces over $ℝ^d$

• Autorzy: R. J. MacG. Dawson
• Języki publikacji: EN

Abstrakty

EN

A Čebyšev set in a metric space is one such that every point of the space has a unique nearest neighbour in the set. In Euclidean spaces, this property is equivalent to being closed, convex, and nonempty, but in other spaces classification of Čebyšev sets may be significantly more difficult. In particular, in hyperspaces over normed linear spaces several quite different classes of Čebyšev sets are known, with no unifying description. Some new families of Čebyšev sets in hyperspaces are exhibited, with dimension d + 1 (where d is the dimension of the underlying space). They are constructed as translational closures of appropriate nested arcs

Kategorie tematyczne

• 52A20: Convex sets in n dimensions (including convex hypersurfaces)
• 41A52: Uniqueness of best approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 84
• Numer: 1
• Strony: 89-110

Daty

wydano

2009

Twórcy

autor

R. J. MacG. Dawson

• Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada

Identyfikatory

DOI

10.4064/bc84-0-6