In this note we prove that a molecule $d(x,y)^{ -1}(\delta(x)-\delta(y))$ is an exposed point of the unit ball of a Lispchitz free space $\mathcal F(M)$ if and only if the metric segment $[x,y]=\{ z \in M \; : \; d(x,y)=d(z,x)+d(z,y) \}$ is reduced to $\{ x,y\}$. This is based on a recent result due to Aliaga and Perneck\'a which states that the class of Lipschitz free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter.
Categories: math.FA