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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-1,
author = {Asuman G\"uven Aksoy and Kyle Edward Kinneberg},
title = {Compact widths in metric trees},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {15-25},
zbl = {1232.54027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-1}
}
Asuman Güven Aksoy; Kyle Edward Kinneberg. Compact widths in metric trees. Banach Center Publications, Tome 95 (2011) pp. 15-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-1/