We present a result which affords the existence of equivalent metrics on a space having distances between certain pairs of points predetermined, with some restrictions. This result is then applied to obtain metric spaces which have interesting properties pertaining to the span, semispan, and symmetric span of metric continua. In particular, we show that no two of these variants of span agree for all simple closed curves or for all simple triods.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-11,
author = {L. C. Hoehn and A. Karassev},
title = {Equivalent metrics and the spans of graphs},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {135-153},
zbl = {1162.54011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-11}
}
L. C. Hoehn; A. Karassev. Equivalent metrics and the spans of graphs. Colloquium Mathematicae, Tome 116 (2009) pp. 135-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-11/