Hostname: page-component-5c6d5d7d68-tdptf Total loading time: 0 Render date: 2024-08-17T21:21:45.064Z Has data issue: false hasContentIssue false
  • English
  • Français

A Helly-type theorem on a sphere

Published online by Cambridge University Press:  09 April 2009

M. J. C. Baker
M. J. C. Baker
Affiliation:
R.A.A.F. Academy Point Cook, Victoria
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to prove that if n+3, or more, strongly convex sets on an n dimensional sphere are such that each intersection of n+2 of them is empty, then the intersection of some n+1 of them is empty. (The n dimensional sphere is understood to be the set of points in n+1 dimensional Euclidean space satisfying x21+x22+ …+x2n+1 = 1.)

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 3 , August 1967 , pp. 323 - 326
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Danzer, L., Grünbaum, B. and Klee, V., ‘Helly's theorem and its relatives’, in Convexity Proceedings Seventh Symposium in Pure Mathematics, American Mathematical Society (A.M.S. Providence R.I. 1963), pp. 101–180.Google Scholar
[2]Helly, E., ‘Über Mengen konvexer Körper mit gemeinschaftlichen Punkten’, Jber. Deutsch. Math.-Verein. 32 (1923), 175–176.Google Scholar
[3]Molnár, J., ‘Über eine Übertragung des Hellyschen Satzes in sphärische Räume’, Acta Math. Acad. Sci. Hungary, 8 (1957), 315–318.CrossRefGoogle Scholar
[4]Rennie, B. C., Unpublished paper.Google Scholar
[5]Robinson, C. V., ‘Spherical theorems of Helly type and congruence indices of spherical caps’. Am. J. Math. 64 (1942), 260–272.CrossRefGoogle Scholar