Continuous functions which take a somewhere dense set of values on every open set
by
Maxim R. Burke
University of Prince Edward Island

We study the class of Tychonoff spaces that can be mapped continuously into the real line in such a way that the preimage of every nowhere dense set is nowhere dense. We show that every metric space without isolated points is in this class. We also give examples of spaces which have nowhere constant continuous maps into the real line and are not in this class.

Date received: October 1, 1998

Copyright © 1998 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 # cabr-09.