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 SM ISO690:2012SOLTAN, Valeriu. On Grünbaum's problem about inner illumination of convex bodies. In: Acta Mathematica Hungarica, 1995, vol. 69, pp. 15-25. ISSN 0236-5294. DOI: https://doi.org/10.1007/BF01874604 |
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  Acta Mathematica Hungarica |
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| Volumul 69 / 1995 / ISSN 0236-5294 | ||||||
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| DOI:https://doi.org/10.1007/BF01874604 | ||||||
| Pag. 15-25 | ||||||
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A set F C bd K is called by P. Soltan [3] an (inner) illuminating set of a convex body K C E d (i.e. a compact convex set with n o n e m p t y interior) provided for every point x C bd K there is a point y C F such that x it y and the open line interval ]x,y[ is contained in int g . P. Soltan (see [3], [4]) posed the problem on the least number of points in an illuminating set of a convex body in E d, and he has proved that this m i n i m u m number is at most d + 1, with d + 1 characterizing simplices. |
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