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Metric Spaces of Extreme Points

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Ernie Manes

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.

Published 2020-10-30.

http://www.tac.mta.ca/tac/volumes/35/49/35-49.pdf

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