Compact widths in metric trees

Asuman Güven Aksoy, and Kyle Edward Kinneberg. "Compact widths in metric trees." Banach Center Publications 92.1 (2011): 15-25. <http://eudml.org/doc/281919>.

@article{AsumanGüvenAksoy2011,
abstract = {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.},
author = {Asuman Güven Aksoy, Kyle Edward Kinneberg},
journal = {Banach Center Publications},
keywords = {metric tree; -widths; compact widths},
language = {eng},
number = {1},
pages = {15-25},
title = {Compact widths in metric trees},
url = {http://eudml.org/doc/281919},
volume = {92},
year = {2011},
}

TY - JOUR
AU - Asuman Güven Aksoy
AU - Kyle Edward Kinneberg
TI - Compact widths in metric trees
JO - Banach Center Publications
PY - 2011
VL - 92
IS - 1
SP - 15
EP - 25
AB - 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.
LA - eng
KW - metric tree; -widths; compact widths
UR - http://eudml.org/doc/281919
ER -