Menger Curve as Inverse Limit
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.
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
Mathematics and Statistics
Keywords and Phrases
Inverse Limit; Set-Valued Functions; Zero-Dimensional
International Standard Serial Number (ISSN)
Article - Journal
© 2021 Elsevier, All rights reserved.
01 Dec 2021