Uniformly antisymmetric function with bounded range

by Ciesielski and Shelah. [CiSh:680]
Real Analysis Exchange, 1998--99
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 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.


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