Fixed-Points in Cech-Stone Remainder
by
Michael A. van Hartskamp
Amsterdam Free University

We present two examples of nice normal spaces X having the property that for some fixed-point free homeomorphism on X its Cech-Stone extension has a fixed point. One of the spaces presented here is locally countable, locally compact, separable, normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this example however requires the Continuum Hypothesis. Since for paracompact spaces with finite covering dimension every fixed-point free homeomorphism has a fixed-point free Cech-Stone extension, these results are ``best possible''.

Date received: June 24, 1996

Copyright © 1996 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 # caah-33.