Compact widths in metric trees

• Autorzy: Asuman Güven Aksoy , Kyle Edward Kinneberg
• Języki publikacji: EN

Abstrakty

EN

The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also obtained.

Kategorie tematyczne

• 05C05: Trees
• 47H08: Measures of noncompactness and condensing mappings, K -set contractions, etc.
• 54E45: Compact (locally compact) metric spaces
• 51F99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 15-25

Daty

wydano

2011

Twórcy

autor

Asuman Güven Aksoy

• Claremont McKenna College, Department of Mathematics, Claremont, CA 91711, USA

autor

Kyle Edward Kinneberg

• University of California, Los Angeles, Department of Mathematics, Los Angeles, CA 90095, USA

Identyfikatory

DOI

10.4064/bc92-0-1