### 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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