Cobos, A. and Navas, L.M. (2021) Tilings of the infinite p-ary tree and Cantor homeomorphisms. Mediterranean Journal of Mathematics, 18 (5). 226. ISSN 1660-5446
Abstract
We define a notion of tiling of the full infinite p-ary tree, establishing a series of equivalent criteria for a subtree to be a tile, each of a different nature; namely, geometric, algebraic, graph-theoretic, order-theoretic, and topological. We show how these results can be applied in a straightforward and constructive manner to define homeomorphisms between two given spaces of p-adic integers, Zp and Zq, endowed with their corresponding standard non-archimedean metric topologies.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2021 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Trees; Tilings; Cantor spaces; Monoid of words; p-adic integers |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Oct 2021 14:38 |
Last Modified: | 07 Oct 2021 14:38 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s00009-021-01854-x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178831 |
Download
Filename: Cobos and Navas, 2021. Tilings of the Infinite p-ary Tree and Cantor Homeomorphisms.pdf
Licence: CC-BY 4.0