On colorings of topological groups
by
M.A. van Hartskamp
Vrije Universiteit Amsterdam
Coauthors: Jan van Mill

This talk is about the question whether there exists a (strongly zero-dimensional) normal topological group G and a fixed-point free homeomorphism f: G --> G for which the Cech-Stone extension \betaf has a fixed point (or equivalently whether f can't be colored). We discuss various approaches:

• Using the construction of the free Boolean group of a space, we can reduce the problem to finding an ordinary example with normal and pseudocompact powers.
• Reasonable sigma products can be shown not to work,
• Neither do reasonable modifications of Hajnal-Juhász groups.

Date received: July 14, 1997

Copyright © 1997 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 # caap-04.