Vol. 21, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On the union of two starshaped sets

D. G. Larman

Vol. 21 (1967), No. 3, 521–524
Abstract

Let S be a compact subset of a topological linear space. We shall say that S has the property φ if there exists a line segment R such that each triple of points x,y and z in S determines at least one point p of R (depending on x,y and z) such that at least two of the segments xp,yp and zp are in S. It is clear that if S is the union of two starshaped sets then S has the property φ, and the problem has been raised by F. A. Valentine [1] as to whether the property φ ensures that S is the union of two starshaped sets. We shall show that this is not so, in general, but we begin by giving a further constraint which ensures the result.

Mathematical Subject Classification
Primary: 52.30
Milestones
Received: 22 December 1965
Revised: 2 May 1966
Published: 1 June 1967
Authors
D. G. Larman