Eberly College of Arts and Sciences
The goal of this note is to construct a uniformly antisymmetric function f : R → R with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson . (See also the list of problems in Thomson  and Problem 2(b) from Ciesielski’s survey .) A problem of existence of uniformly antisymmetric function f : R → R with finite range remains open.
Digital Commons Citation
Ciesielski, Krzysztof, "Uniformly Antisymmetric Function With Bounded Range" (1999). Faculty & Staff Scholarship. 830.