Vol. 33, No. 3, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 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
Wild points of cellular arcs in 2-complexes in E3 and cellular hulls

Gail Atneosen

Vol. 33 (1970), No. 3, 551–553
Abstract

Loveland has established that if W is the set of wild points of a cellular arc that lies on a 2-sphere in E8, then either W is empty, W is degenerate, or W contains an arc. This note considers 2-complexes rather than 2-spheres. Making strong use of Loveland’s results and others, it is proved that a cellular arc in a 2-complex in E8 either contains an arc of wild points or has at most one wild point that has a neighborhood in the 2-complex homeomorphic to an open 2-cell. In the case of noncellular arcs in E3, one can investigate “minimal cellular sets” containing the arc. A cellular hull of a subset A of Es is a cellular set containing A such that no proper cellular set also contains A. A characterization is given of those arcs in E3 that have cellular hulls that lie in tame 2-complexes in E3.

Mathematical Subject Classification
Primary: 54.78
Milestones
Received: 22 October 1969
Published: 1 June 1970
Authors
Gail Atneosen