On the Notion of Tree-Likeness for Generalized Continua
Abstract
A variety of equivalent approaches to tree-likeness is available in classical continuum theory. In absence of compactness, some of those equivalences do not hold. In this paper, we compare the class of generalized continua defined as inverse limits of locally finite trees with proper bonding maps with the class of those for which any open cover admits acyclic refinements. We show that the latter is precisely the subclass of the former consisting of those generalized continua with exhausting sequences of tree-like continua. In addition, we show that locally injective proper maps onto tree-like generalized continua are homeomorphisms for the second definition but not for the first one, which, notwithstanding, is still reflected by such maps.
Recommended Citation
W. J. Charatonik et al., "On the Notion of Tree-Likeness for Generalized Continua," Topology Proceedings, vol. 54, pp. 305 - 322, Auburn University, Jan 2019.
Department(s)
Mathematics and Statistics
Keywords and Phrases
Acyclic cover; Freudenthal compactification; Generalized continuum; Inverse limit; Proper map; Tree-like
International Standard Serial Number (ISSN)
2331-1290; 0146-4124
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Auburn University, All rights reserved.
Publication Date
01 Jan 2019
