Spaces of Extremal Magnitude

Tom Leinster*, Mark W. Meckes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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, ∞]. Until now, no example with magnitude ∞ 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.
Original languageEnglish
JournalProceedings of the american mathematical society
Publication statusAccepted/In press - 4 Feb 2023


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