## Real Analysis Exchange

### Uniformly Antisymmetric Functions with Bounded Range

#### Abstract

The goal of this note is to construct a uniformly antisymmetric function $f\colon\mathbb{R}\to\mathbb{R}$ with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson [6]. (See also the list of problems in Thomson [9] and Problem 2(b) from Ciesielski's survey [5].) A problem of existence of uniformly antisymmetric function $f\colon\mathbb{R}\to\mathbb{R}$ with finite range remains open.

#### Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 615-620.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285689139

Mathematical Reviews number (MathSciNet)
MR1704738

Zentralblatt MATH identifier
0968.26004

#### Citation

Ciesielski, Krzysztof; Shelah, Saharon. Uniformly Antisymmetric Functions with Bounded Range. Real Anal. Exchange 24 (1999), no. 2, 615--620. https://projecteuclid.org/euclid.rae/1285689139