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Parallel lines associated with two sets

1966
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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What conditions determine when a collection of points A lies on a collection of parallel lines each member of which intersects a set B? In order to describe these conditions the following notations and definitions are used. Also for earlier results see Robkin and Valentine (2). Notations. We use the following abbreviations where E n is ^-dimensional Euclidean space and where S C E n , x £ E n , y G E n : cl 5 = closure of S, int 5 = interior of S, bd 5 = boundary of S, conv S = convex hull of

doi:10.4153/cjm-1966-080-9
fatcat:ubva2coia5gxjbgwhmjwiewmhe