In this note it is proved that the range of uniformly
antisymmetric function must have at least four elements.
This generalizes the results from
[P. Kostyrko, There is no strongly locally antisymmetric set,
*Real Analysis Exchange* 17 (1991-92), 423--425]
and
[K. Ciesielski, L. Larson,
Uniformly antisymmetric functions,
* Real Anal. Exchange 19 * (1993-94), 226-235]
that the range of such function must
have at least three elements. The problem whether the range
of uniformly antisymmetric function can be finite remains open.

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**Last modified July 5, 2001.**