On the asymptotic magnitude of subsets of Euclidean space

Details On the asymptotic magnitude of subsets of Euclidean space On the asymptotic magnitude of subsets of Euclidean space

2009-08-11

arxiv.org/abs/0908.1582v1

Mathematics

Metric Geometry

20 pages

Scientific paper

'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.

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