We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of 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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-3-4,
author = {Aleksander Maliszewski},
title = {Separating sets by Darboux-like functions},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {271-283},
zbl = {1017.26002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-3-4}
}
Aleksander Maliszewski. Separating sets by Darboux-like functions. Fundamenta Mathematicae, Tome 173 (2002) pp. 271-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-3-4/