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New Characterizations of Polyhedral Cones

Published online by Cambridge University Press:  20 November 2018

H. Mirkil
H. Mirkil*
Affiliation:
Dartmouth College Hanover, NIL
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A pyramid clearly has all its projections closed, even when the line segments from vertex to base are extended to infinite half-lines. Not so a circular cone. For if the cone is on its side and supported by the (x, y) plane in such a way that its infinite half-line of support coincides with the positive x axis, then its horizontal projection on the (y, z) plane is the open upper half-plane y > 0, together with the single point (0, 0).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 1 - 4
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. de Leeuw, K., A type of convexity in the space of n complex variables, Trans. Amer. Math. Soc. (to appear).Google Scholar
2. Fenchel, W., Convex cones, sets, and functions, Princeton lecture notes (mimeographed) 1953.Google Scholar
3. Weyl, H., Elemenädre Theorie der konvexen Polyeder, Comm. Math. Helv. 7 (1935), 290.Google Scholar