The Magnitude of Metric Spaces

@inproceedings{Leinster2013TheMO,
  title={The Magnitude of Metric Spaces},
  author={Tom Leinster},
  year={2013}
}
Magnitude is a real-valued invariant of metric spaces, analogous to Euler characteristic of topological spaces and cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies the analogies between cardinalitylike invariants in mathematics. Although this motivation is a world away from geometric measure, magnitude, when applied to subsets of R, turns out to be intimately related to invariants such as volume, surface area, perimeter and… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 49 references

Positive definite metric spaces

  • M. W. Meckes
  • Positivity, in press,
  • 2013
Highly Influential
10 Excerpts

Metric Structures for Riemannian and Non-Riemannian Spaces

  • M. Gromov
  • 2001
Highly Influential
4 Excerpts

Notions of Möbius inversion

  • T. Leinster
  • Bulletin of the Belgian Mathematical Society,
  • 2012
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…