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For a complete metric space , we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space are precisely the elementary molecules defined by pairs of points in such that the triangle inequality is strict for any different from and . To this end, we show that the class of Lipschitz-free spaces over closed subsets of is closed under arbitrary intersections when has finite diameter, and that this allows a natural definition of the support of elements of .
Cite this article
Ramón J. Aliaga, Eva Pernecká, Supports and extreme points in Lipschitz-free spaces. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 2073–2089DOI 10.4171/RMI/1191