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Iterated function spaces and Lindelöf \Sigma-property
by
Vladimir V. Tkachuk
Universidad Autonoma Metropolitana de Mexico
We prove that if Cp(X) is a Lindelöf \Sigma-space, then so is Cp(\nuX), where \nuX is the Hewitt realcompactification of the space X. One of the important consequences is that if Cp(X) is a Lindelöf \Sigma-space, then Cp, n(X) is a Lindelöf \Sigma-space for every odd n. Another consequence is that if the second Cp is a Lindelöf \Sigma-space, then so are all even Cp's.
The results in question show that there are only four possibilites for the distribution of the Lindelöf \Sigma-property in iterated function spaces:
1) no iterated function space is a Lindelöf \Sigma-space;
2) all iterated function spaces are Lindelöf \Sigma-spaces;
3) only even iterated function spaces are Lindelöf \Sigma-spaces;
4) only odd iterated function spaces are Lindelöf \Sigma-spaces;
Date received: May 17, 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 # cacl-13.