Description: given n-dimensional space of m-space points S1, ..., Sm, if L straight sets with each point are public, It claimed L m point set of a straight line through the (line transversal or stabbin g line). Similarly, if K Line (Line of this paper are to the closing segment, which includes single-point set) and each points are public, claimed for the K m of a point set across the line (or stab segment transversal bing line segment). The concept of across Hailai theorem (Helly's theorem) extension The existence of such issues has been calculated geometry theorem Hailai category (Helly-type theorems ) theory ([1], [2]) and the algorithm ([3], [4]) research.
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