Vol. 24, No. 3, 1968

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
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Point-like 0-dimensional decompositions of S3

Howard Wilson Lambert and Richard Benjamin Sher

Vol. 24 (1968), No. 3, 511–518

This paper is concerned with upper semicontinuous decompositions of the 3-sphere which have the property that the closure of the sum of the nondegenerate elements projects onto a set which is 0-dimensional in the decomposition space. It is shown that such a decomposition is definable by cubes with handles if it is point-like. This fact is then used to obtain some properties of point-like decompositions of the 3-sphere which imply that the decomposition space is a topological 3-sphere. It is also shown that decompositions of the 3-sphere which are definable by cubes with one hole must be pointlike if the decomposition space is a 3-sphere.

Mathematical Subject Classification
Primary: 54.78
Received: 25 July 1966
Published: 1 March 1968
Howard Wilson Lambert
Richard Benjamin Sher