Vol. 23, No. 1, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A spherical Helly-type theorem

M. J. C. Baker

Vol. 23 (1967), No. 1, 1–3
Abstract

The purpose of this paper is to prove for all positive integers n and r that if a family of n + 1 + 2r, or more, strongly convex sets on the n dimensional sphere Sn is such that each intersection of n + 1 + r of them is empty, then the intersection of some n + 1 of them must be empty. (Sn is the set of points in n + 1 dimensional Euclidean space satisfying x12 + x22 + + xn+1l = 1. A set on a sphere is called strongly convex if it does not contain any pair of diametrically opposite or antipodal points, and if together with any two of its points it contains the whole of the minor arc of the great circle joining them.)

Mathematical Subject Classification
Primary: 52.34
Milestones
Received: 5 August 1966
Published: 1 October 1967
Authors
M. J. C. Baker