Abstract
We deal with an analogue of the cone = hyperspace property for generalized continua. Namely, we study the class Cyl of those generalized continua X for which the hyperspace C(X) is homeomorphic to the infinite cylinder X×R≥0. The class Cyl is characterized by using continuous selections and compactwise Whitney maps, extending a theorem due to Illanes to the non-compact setting. Also it is shown that Cyl contains all 1-dimensional atriodic Kelley generalized continua whose constituants are one-to-one continuous images of the line R.
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