Connectivity functions and images on Peano continua
J. Cornette (1966)
Fundamenta Mathematicae
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Connectivity functions and images on Peano continua
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Size levels for arcs
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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.