Vol. 34, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 311: 1
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
On the number of nonpiercing points in certain crumpled cubes

Robert Jay Daverman

Vol. 34 (1970), No. 1, 33–43
Abstract

Let K denote the closure of the interior of a 2-sphere S topologically embedded in Euclidean 3-space E8. If K S is an open 3-cell, McMillan has proved that K has at most one nonpiercing point. In this paper we use a more general condition restricting the complications of K S to describe the number of nonpiercing points. The condition is this: for some fixed integer nK S is the monotone union of cubes with n holes. Under this hypothesis we find that K has at most n nonpiercin g points (Theorem 5). In addition, the complications of K S are induced just by these nonpiercing points. Generally, at least two such points are required, for otherwise n = 0 (Theorem 3).

Mathematical Subject Classification
Primary: 54.78
Milestones
Received: 4 June 1969
Revised: 14 November 1969
Published: 1 July 1970
Authors
Robert Jay Daverman