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|MAXIM R. BURKE, University of Prince Edward Island|
|Continuous functions which take a somewhere dense set of values on every open set|
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.