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Some Properties of C-Convex Sets

Published online by Cambridge University Press:  20 November 2018

F. A. Valentine
F. A. Valentine*
Affiliation:
University of California at Los Angeles
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The notion of convexity in (m-dimensional Euclidean spaces) can be generalized to apply to non-connected sets as follows.

A set is said to be C-convex if each of its components is convex. If the number of components of such a set is n, it is called a Cn-convex set.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 481 - 488
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Bonnesen, and Fenchel, Theorie der Konvexen Korper (New York, 1948).Google Scholar
[2] Horn, Alfred and Valentine, F. A., some properites of L sets in the plane, Duke Math.J., vol.16(1949), 131–140.Google Scholar
[3] Newmam, M. H. A., Elements of the topology of plane set of points (Cambridge, 1939).Google Scholar