✦ LIBER ✦

Continuous functions which take a somewhere dense set of values on every open set

✍ Scribed by Maxim R. Burke

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 161 KB
Volume: 103
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00163-1

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✦ Synopsis

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.