Vol. 48, No. 1, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 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 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A compact set that is locally holomorphically convex but not holomorphically convex

Michael Benton Freeman and Reese Harvey

Vol. 48 (1973), No. 1, 77–81
Abstract

It is shown that a certain simple imbedding T of the ordinary two-dimensional torus in C2 contains a polynomially convex compact T-neighborhood of each of its points, but T is not holomorphically convex in even the weakest presently accepted sense. This example illustrates some of the limitations of a theory of lower dimensional sets in Cn. In particular, it shows the difficulty of developing a theory based on local information.

Mathematical Subject Classification 2000
Primary: 32E30
Secondary: 32E20
Milestones
Received: 22 June 1972
Published: 1 September 1973
Authors
Michael Benton Freeman
Reese Harvey