Polyhedral compactifications
23.06.2020 -
The preprint "Polyhedral compactifications, I" by Corina Ciobotaru, Linus Kramer and Petra Schwer was recently updated on the arXiv.
Link to the paper: arXiv.
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 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.