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arXiv · 2112.12889

Spaces of extremal magnitude

Tom Leinster·Mark Meckes
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Abstract

Magnitude is a numerical invariant of compact metric spaces. Its theory is most mature for spaces satisfying the classical condition of being of negative type, and the magnitude of such a space lies in the interval $[1, \infty]$. Until now, no example with magnitude $\infty$ was known. We construct some, thus answering a question open since 2010. We also give a sufficient condition for the magnitude of a space to converge to 1 as it is scaled down to a point, unifying and generalizing previously known conditions.

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Tom Leinster, Mark Meckes. 2021-12-24. Spaces of extremal magnitude. https://doi.org/10.1090/proc%2F16433

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