Abstract
We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of cube complexes. Examples of median spaces with compact intervals include all finite-rank median spaces and all proper median spaces of infinite rank. Our methods also apply to general median algebras, where we recover the zero-completions of Bandelt and Meletiou (1993). Along the way, we prove various properties of halfspaces in finite-rank median spaces and a duality result for locally convex median spaces.
Citation
Elia Fioravanti. "Roller boundaries for median spaces and algebras." Algebr. Geom. Topol. 20 (3) 1325 - 1370, 2020. https://doi.org/10.2140/agt.2020.20.1325
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