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Polyhedral compactifications, I

  • Corina Ciobotaru , Linus Kramer EMAIL logo und Petra Schwer
Veröffentlicht/Copyright: 11. August 2023
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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, by 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.

  1. Communicated by: R. Weiss

Acknowledgements

The authors would like to thank Andreas Berning, Siegfried Echterhoff, Gaiane Panina and the referee for helpful remarks.

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Received: 2022-10-04
Revised: 2023-05-02
Published Online: 2023-08-11
Published in Print: 2023-08-28

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