We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
@article{bwmeta1.element.bwnjournal-article-fmv141i3p243bwm,
author = {Sam Nadler and T. West},
title = {Size levels for arcs},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {243-255},
zbl = {0856.54034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p243bwm}
}
Nadler, Sam; West, T. Size levels for arcs. Fundamenta Mathematicae, Tome 141 (1992) pp. 243-255. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p243bwm/
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