Continuously Ray Extendible Continua and Spirals to Solenoids
by
C. Wayne Proctor
Stephen F. Austin State University

A continuum M is defined to be continuously ray extendible if and only if it is true that for each mapping f which maps a continuum X onto M and for each compactification of a half line L that has remainder M, there exists a compactification of a half line R that has remainder X such that f has a continuous extension F which maps X \cup R onto M \cup L. It is known that each solenoid that is not a circle is continuously ray extendible. If M is the compactification of the union of a countable collection {M₁, M₂, M₃, ...} of continua such that M_i subset or equal M_i+1 for each natural number i, the remainder of the compactification is a solenoid C with odd bonding maps, and there is a mapping \phi from M onto the unit complex circle with the property that \phi|_C is essential and there exists a lift \theta defined on M - C relative to \phi, then it will be shown that M is not a continuously ray extendible continuum.

Date received: January 27, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-18.