Menger Curve as Inverse Limit
Abstract
We show that the Menger curve can be represented as a set-valued inverse limit of intervals [0,1] with a single bonding function. The graph of the function is homeomorphic to the Sierpiński carpet. This answers a question by M. Hiraki and H. Kato.
Recommended Citation
W. J. Charatonik and Ş. Şahan, "Menger Curve as Inverse Limit," Topology and its Applications, article no. 107788, Elsevier, Dec 2021.
The definitive version is available at https://doi.org/10.1016/j.topol.2021.107788
Department(s)
Mathematics and Statistics
Keywords and Phrases
Inverse Limit; Set-Valued Functions; Zero-Dimensional
International Standard Serial Number (ISSN)
0166-8641
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2021 Elsevier, All rights reserved.
Publication Date
01 Dec 2021
