Polyhedral compactifications, I

Corina-Gabriela Ciobotaru; Linus Kramer; Petra Schwer

doi:10.1515/advgeom-2023-0018

Polyhedral compactifications, I

Corina-Gabriela Ciobotaru, Linus Kramer^*, Petra Schwer

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

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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.

Originalsprog	Engelsk
Tidsskrift	Advances in Geometry
Vol/bind	23
Nummer	3
Sider (fra-til)	413-436
Antal sider	24
ISSN	1615-715X
DOI	https://doi.org/10.1515/advgeom-2023-0018
Status	Udgivet - 1 aug. 2023

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10.1515/advgeom-2023-0018

https://arxiv.org/pdf/2002.12422

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AB - 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.

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Polyhedral compactifications, I

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