Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum with . This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
@article{bwmeta1.element.bwnjournal-article-fmv150i1p17bwm,
author = {Michael Levin and Yaki Sternfeld},
title = {Hyperspaces of two-dimensional continua},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {17-24},
zbl = {0858.54006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p17bwm}
}
Levin, Michael; Sternfeld, Yaki. Hyperspaces of two-dimensional continua. Fundamenta Mathematicae, Tome 149 (1996) pp. 17-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p17bwm/
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