Hyperspaces of Generalized Continua which Are Infinite Cylinders
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 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.
W. J. Charatonik et al., "Hyperspaces of Generalized Continua which Are Infinite Cylinders," Topology and its Applications, vol. 267, Elsevier B.V., Nov 2019.
The definitive version is available at https://doi.org/10.1016/j.topol.2019.106829
Mathematics and Statistics
Keywords and Phrases
(Generalized) Continuum; Cone=hyperspace Property; Constituant; Hyperspace; Kelley Property; Proper Map
International Standard Serial Number (ISSN)
Article - Journal
© 2019 Elsevier B.V., All rights reserved.
01 Nov 2019