Abstract
We introduce a metric \(d_c\) on the Busemann space (X, d) such that the horofunction compactification of the space \((X, d_c)\) is equivalent to the geodesic compactification of the initial space. The space \((X, d_c)\) is not geodesic in general. It is shown that \((X, d_c)\) is geodesic if and only if X is a real tree.
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The work was supported by RFBR, Grant 14-01-00219.
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Andreev, P. The cone metric of a Busemann space. J. Geom. 109, 25 (2018). https://doi.org/10.1007/s00022-018-0430-6
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DOI: https://doi.org/10.1007/s00022-018-0430-6