Coloring fixed-point free maps
by
J. M. Aarts
TU Delft
Coauthors: Robbert Fokkink, Hans Vermeer

A fixed-point free map f : X --> X is said to be colorable with k colors if there exists a closed cover C of X consisting of k elements such that C \cap f(C) = \emptyset for every C in C.

A fixed-point free map f can be extended to a fixed-point free map of the Cech-Stone compactification if anf only if f is colorable.

It is shown that each fixed-point free involution of a paracompact Hausdorff space X with dimX <= n can be colored with n+2 colors. Each fixed-point free homeomorphism of a metrizable space X with dimX <= n is colorable with n+3 colors. Every fixed-point free continuous selfmap of a compact metrizable space X with dimX <= n can be colored with n+3 colors.

Date received: August 14, 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 Mathematical Conference Abstracts. Document # caaj-54.