Inverse Limits With Set-valued Functions Having Graphs That Are Arcs

Author

W. (William) T. (Thomas) Ingram, Missouri University of Science and TechnologyFollow

Abstract

Banič and Kennedy (2015) [8] have drawn attention to a natural but largely unexplored field of study in the theory of inverse limits with set-valued functions, namely using bonding functions having graphs that are arcs. At the end of that paper they pose a question: If f:[0,1]→2[0,1] is an upper semi-continuous function such that G(fn) is connected for each n and G(f) is an arc, is lim←f connected? In this paper we provide a negative answer to that question, include some additional examples as well as a theorem on trivial shape (not requiring that the graphs be arcs), and pose several questions concerning, for the most part, inverse limits with set-valued functions whose graphs are arcs.

Recommended Citation

W. T. Ingram, "Inverse Limits With Set-valued Functions Having Graphs That Are Arcs," Topology and its Applications, vol. 299, article no. 107737, Elsevier, Aug 2021.

The definitive version is available at https://doi.org/10.1016/j.topol.2021.107737

Department(s)

Mathematics and Statistics

Keywords and Phrases

Continuum; Graphs that are arcs; Inverse limit; Set-valued function; Trivial shape

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Elsevier, All rights reserved.

Publication Date

01 Aug 2021