On the asymptotic magnitude of subsets of Euclidean space

Tom Leinster, Simon Willerton

Research output: Contribution to journalArticlepeer-review

Abstract

Magnitude is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of Euclidean space with finite subsets, the magnitudes of line segments, circles and Cantor sets are defined and calculated. It is observed that asymptotically these satisfy the inclusion-exclusion principle, relating them to intrinsic volumes of polyconvex sets.
Original languageEnglish
Pages (from-to)287
Number of pages310
JournalGeometriae Dedicata
Volume164
DOIs
Publication statusPublished - 2013

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