Abstract
This chapter introduces a strongly proximal version of Helly’s theorem for convex sets and convex bodies. The collection of labelled Voronoï regions in the mesh nerve on the apple surface in Fig. 11.1 is an example of a Helly family of convex bodies.
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Notes
- 1.
E.W. Weisstein, polyform, Mathworld–A Wolfram web resourcem, http://mathworld.wolfram.com/Polyform.html.
- 2.
For much more about this, see http://mathworld.wolfram.com/Polyiamond.html.
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Peters, J.F. (2016). Helly’s Theorem and Strongly Proximal Helly Theorem. In: Computational Proximity. Intelligent Systems Reference Library, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-30262-1_11
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DOI: https://doi.org/10.1007/978-3-319-30262-1_11
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