Tilings of the infinite $p$-ary tree and Cantor homeomorphisms
General Topology
2021-09-23 v2 Combinatorics
Dynamical Systems
Rings and Algebras
Abstract
We define a notion of tiling of the full infinite -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 -adic integers, and , endowed with their corresponding standard non-archimedean metric topologies.
Keywords
Cite
@article{arxiv.1911.00929,
title = {Tilings of the infinite $p$-ary tree and Cantor homeomorphisms},
author = {Alberto Cobos and Luis M. Navas},
journal= {arXiv preprint arXiv:1911.00929},
year = {2021}
}
Comments
Previous version: 13 pages. Latest version: 11 pages. We have restructured the article. The non-topological considerations have been collected in section 2 and the topological considerations are now in section 3