Separating sets by Darboux-like functions
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 271-283
MSC: Primary 26A21, 54C30; Secondary 26A15, 54C08.
DOI: 10.4064/fm175-3-4
Abstract
We consider the following problem: Characterize the pairs $\langle A, B \rangle$ of subsets of ${\mathbb R}$ which can be separated by a function from a given class, i.e., for which there exists a function $f$ from that class such that $f=0$ on $A$ and $f=1$ on $B$ (the classical separation property) or $f<0$ on $A$ and $f>0$ on $B$ (a new separation property).
