It is shown that any compact metric space of diameter at most 2 embeds isometrically as a linearly independent set of extreme points of the unit ball of a separable Banach space. The proof illustrates how category theory can play a useful role in a problem of functional analysis.
Keywords: free Banach space, Arens-Eells embedding, extreme point
2020 MSC: 46B04, 46B50, 18A40
Theory and Applications of Categories, Vol. 35, 2020, No. 49, pp 1823-1832.