# Compact widths in metric trees

Asuman Güven Aksoy; Kyle Edward Kinneberg

Banach Center Publications (2011)

- Volume: 92, Issue: 1, page 15-25
- ISSN: 0137-6934

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topAsuman 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 -

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