Continuous functions which take a somewhere dense set of values on every open set
Burke, Maxim R.
Topology and its Applications
Mathematics and Statistics
We study the class of Tychonoff spaces that can be mapped continuously into R 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 R and are not in this class. (C) 2000 Elsevier Science B.V. All rights reserved.