Title

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.

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

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