Year: 2023
Type: article
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.
DOI: 10.1090/proc/16433
Authors: Tom Leinster, Mark Meckes
Institutions: University of Edinburgh, Case Western Reserve University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4382025543