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Distances on Convex Bodies, Cones, and Simplicial Complexes

In: Encyclopedia of Distances

Author

Listed:
  • Michel Marie Deza

    (École Normale Supérieure)

  • Elena Deza

    (Moscow State Pedagogical University)

Abstract

A convex body in the n-dimensional Euclidean space $\mathbb{E}^{n}$ is a compact convex subset of $\mathbb{E}^{n}$ . It is called solid (or proper) if it has nonempty interior. Let K denote the space of all convex bodies in $\mathbb{E}^{n}$ , and let K p be the subspace of all proper convex bodies.

Suggested Citation

  • Michel Marie Deza & Elena Deza, 2013. "Distances on Convex Bodies, Cones, and Simplicial Complexes," Springer Books, in: Encyclopedia of Distances, edition 2, chapter 0, pages 169-180, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-30958-8_9
    DOI: 10.1007/978-3-642-30958-8_9
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