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Parallel Lines Associated with Two Sets

Published online by Cambridge University Press:  20 November 2018

Eugene Robkin  and
F. A. Valentine
Eugene Robkin
Affiliation:
University of California at Los Angeles
F. A. Valentine
Affiliation:
University of California at Los Angeles
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 811 - 816
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Helly, E., Über Mengen konvexer Körper mit gemeinschaftlichen Punkten, Jber. Deutsch. Math. Verein., 32 (1923), 175–176.Google Scholar
2. Robkin, E. and Valentine, F. A., Families of parallel lines associated with sets, Pac. J. Math., 16 (1966), 147–157.Google Scholar
3. Valentine, F. A., Convex sets (New York, 1964).Google Scholar