Hyperspaces of Generalized Continua which Are Infinite Cylinders

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 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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

(Generalized) Continuum; Cone=hyperspace Property; Constituant; Hyperspace; Kelley Property; Proper Map

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Elsevier B.V., All rights reserved.

Publication Date

01 Nov 2019

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