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• # Artykuł - szczegóły

## Banach Center Publications

2009 | 84 | 1 | 89-110

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

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

89-110

wydano
2009

### Twórcy

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