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The
horofunction compactification of $\ell^{1}$-products of
metric spaces
Bas Lemmens, Cam Milliken and Kieran Power |
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Vol. 19 (2026), No. 1, 145–160
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Abstract |
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We study the horofunction compactification of the -product of proper geodesic metric spaces. We provide a complete characterisation of the horofunction compactification of the product space in terms of the horofunctions of the constituent spaces, and provide a complete characterisation of the Busemann points in terms of the Busemann points of the constituent spaces. We also identify the parts of the horofunction boundary and the detour distance. The results are applied to show that the horofunction compactification of the -product of finite-dimensional normed spaces with polyhedral or smooth unit balls is naturally homeomorphic to the closed dual unit ball. |
Keywords
horofunctions, metric spaces, products, Busemann points
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Mathematical Subject Classification
Primary: 51F99, 53C60
Secondary: 46B20
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Milestones
Received: 6 June 2024
Accepted: 18 July 2024
Published: 25 January 2026
Communicated by Gaven Martin
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Authors |
| Bas Lemmens | |
| School of Mathematics, Statistics
& Actuarial Science University of Kent Canterbury United Kingdom |
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| Cam Milliken | |
| School of Mathematics, Statistics
& Actuarial Science University of Kent Canterbury United Kingdom |
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| Kieran Power | |
| School of Mathematics, Statistics
& Actuarial Science University of Kent Canterbury United Kingdom |
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| © 2026 MSP (Mathematical Sciences Publishers). |
