On the asymptotic magnitude of subsets of Euclidean space

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.

• Publication year

  2009

• Venue

  Geometriae Dedicata

• Publication date

  2009-08-11

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1007/s10711-012-9773-6arXiv 0908.1582
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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