Uniformly antisymmetric function with bounded range

by

Krzysztof Ciesielski, Saharon Shelah

Real Anal. Exchange 24(2) (1998-99), 615-619.

We construct a uniformly antisymmetric function f:R-->R with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson (Uniformly antisymmetric functions, Real Anal. Exchange 19 (1993--94), 226-235). A problem of existence of uniformly antisymmetric function f:R-->R with finite range remains open.

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Last modified August 25, 1999.