The Magnitude of Metric Spaces

  title={The Magnitude of Metric Spaces},
  author={Tom Leinster},
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


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