Daniilidis, A., Garrido, M. I., Jaramillo, J. A., & Tapia Garcia, S. (2025). Horofunction extension and metric compactifications. Transactions of the American Mathematical Society Series B, 12, 1130–1155. https://doi.org/10.1090/btran/234
A necessary and sufficient condition for the horofunction extension (X, d)h of a metric space (X, d) to be a compactification is hereby established. The condition clarifies previous results on proper metric spaces and geodesic spaces and yields the following characterization: a Banach space is Gromovcompactifiable under any renorming if and only if it does not contain an isomorphic copy of ℓ¹ . In addition, it is shown that, up to an adequate renorming, every Banach space is Gromov-compactifiable. Therefore, the property of being Gromov-compactifiable is not invariant under bi-Lipschitz equivalence.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
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Project (external):
MICINN grant (Spain) MinisteriodeCiencia, Innovaci´onyUniversidades(Spain)grant
