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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Some properties of families of convex cones
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by Meir Katchalski PDF
Trans. Amer. Math. Soc. 233 (1977), 235-240 Request permission

Abstract:

The purpose of this paper is to study properties of finite families of convex cones in n-dimensional Euclidean space ${R^n}$, whose members all have the origin as a common apex. Of special interest are such families of convex cones in ${R^n}$ which have the following property: Each member of the family is of dimension n, the intersection of any two members is at least $(n - 1)$-dimensional, ..., the intersection of any n members is at least 1-dimensional and the intersection of all the members is the origin.
References
  • M. J. C. Baker, A spherical Helly-type theorem, Pacific J. Math. 23 (1967), 1–3. MR 222770, DOI 10.2140/pjm.1967.23.1
  • B. Grünbaum, Convex polytopes, Interscience, New York, 1967. MR 37 #2085.
  • M. Katchalski, Reconstructing dimensions of intersections of convex sets, Aequationes Math. 17 (1978), no. 2-3, 249–254. MR 500552, DOI 10.1007/BF01818564
  • —, Non-degenerate families of convex cones and convex polytopes, Discrete Math. (to appear). —, On a Helfy type theorem of M. J. C. Baker, Proc. Amer. Math. Soc. (to appear).
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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