Polyhedral compactifications, I
Metric Geometry
2023-05-05 v4 Geometric Topology
Abstract
In this work we describe horofunction compactifications of metric spaces and finite dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral norms by means of nonstandard methods, that is, ultrapowers of the spaces at hand. The polyhedral compactifications of the vector spaces carry the structure of stratified spaces with the strata indexed by dual faces of the polyhedral unit ball. Explicit neighborhood bases and descriptions of the horofunctions are provided.
Cite
@article{arxiv.2002.12422,
title = {Polyhedral compactifications, I},
author = {Corina Ciobotaru and Linus Kramer and Petra Schwer},
journal= {arXiv preprint arXiv:2002.12422},
year = {2023}
}
Comments
30 pages; v2: Additional references and new results added, small errors corrected; v3: updated references; v4: minor changes, figures added, final and published draft - to appear in Advances in Geometry