Size levels for arcs
Volume 141 / 1992
Fundamenta Mathematicae 141 (1992), 243-255
DOI: 10.4064/fm-141-3-243-255
Abstract
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.
