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2000 Summer Conference on Topology and its Applications (Topo2000)
July 26-29, 2000
Miami University
Oxford, OH, USA |
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Organizers
Dennis Burke, Zoltan Balogh, Sheldon Davis
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Colorings of spaces and maps.
by
J. Vermeer
Technical University of Delft, Netherlands
Coauthors: J.A.M. de Groot, J.M. Aarts, R.J. Fokkink
We investigate for involutions \sigma:X --> X colorings of the
subspaces A. i.e. finite coverings A1, ... , Ak with
Ai \cap \sigma(Ai)=\emptyset. One of the results is that there
is a difference of behaviour between the relative closed
colorings, the relative open colorings and the open colorings of
A. Upperbounds in terms of the dimension of the subspace are
obtained and an example is provided that shows that the obtained
upperbounds are best possible. Moreover, we construct an example
with finite relative closed coloring number, finite relative open
coloringnumber but infinite open coloring number and an
example with finite relative closed coloring number but infinite
relative open coloringnumber.
Date received: March 21, 2000
Copyright © 2000 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 # caeu-02.