Some properties of families of convex cones
Author:
Meir Katchalski
Journal:
Trans. Amer. Math. Soc. 233 (1977), 235-240
MSC:
Primary 52A20
DOI:
https://doi.org/10.1090/S0002-9947-1977-0493755-3
MathSciNet review:
0493755
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Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this paper is to study properties of finite families of convex cones in n-dimensional Euclidean space , whose members all have the origin as a common apex.
Of special interest are such families of convex cones in which have the following property: Each member of the family is of dimension n, the intersection of any two members is at least
-dimensional, ..., the intersection of any n members is at least 1-dimensional and the intersection of all the members is the origin.
- [1] M. J. C. Baker, A spherical Helly-type theorem. Pacific J. Math. 23 (1967), 1-3. MR 36 #5820. MR 0222770 (36:5820)
- [2] B. Grünbaum, Convex polytopes, Interscience, New York, 1967. MR 37 #2085.
- [3] M. Katchalski, Reconstructing dimensions of intersections of convex sets, Aequationes Math. (to appear). MR 0500552 (58:18156)
- [4] -, Non-degenerate families of convex cones and convex polytopes, Discrete Math. (to appear).
- [5] -, On a Helfy type theorem of M. J. C. Baker, Proc. Amer. Math. Soc. (to appear).
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1977-0493755-3
Keywords:
Euclidean space,
convex sets
Article copyright:
© Copyright 1977
American Mathematical Society