ON EXPOSED POINTS OF LIPSCHITZ FREE SPACES
Résumé
In this note we prove that a molecule d(x, y) −1 (δ(x) − δ(y)) is an exposed point of the unit ball of a Lispchitz free space F (M) if and only if the metric segment [x, y] = {z ∈ M : d(x, y) = d(z, x) + d(z, y)} is reduced to {x, y}. This is based on a recent result due to Aliaga and Pernecká which states that the class of Lipschitz free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter.
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