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Titlebook: Excursions into Combinatorial Geometry; Vladimir Boltyanski,Horst Martini,Petru S. Soltan Textbook 1997 Springer-Verlag Berlin Heidelberg

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https://doi.org/10.1007/978-94-009-3867-0ameter diam . = sup of the part . is . than diam .. The least positive integer . for which such a partition exists is said to be the . of ., since K. Borsuk considered this question for two-dimensional sets and for the n-dimensional ball . ⊂ R.. One motivation for these investigations was given by t
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https://doi.org/10.1007/978-3-642-45479-0e problems are equivalent for compact, convex bodies, whereas they differ from each other in the unbounded case. Among these four problems, the central one is the question for the minimal number of smaller homothets of a convex body . ⊂ R. which are sufficient to cover.. In addition, the problem of
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0172-5939 Overview: 978-3-540-61341-1978-3-642-59237-9Series ISSN 0172-5939 Series E-ISSN 2191-6675
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-Convexity in normed spaces,nvex sets (§10) and the properties of .-convex flats (§11). This chapter is of decisive importance for developing a machinery for solving combinatorial problems. Nevertheless, it is interesting for itself, because the family of .-convex sets has far-reaching analogies to the family of convex sets in
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-convexity,merges for the possibility of neglecting a norm (by which .-convex half-spaces are introduced) in order to find other ways to describe half-spaces whose intersections determine certain classes of convex sets.
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