Open Access
1998/1999 Uniformly Antisymmetric Functions with Bounded Range
Krzysztof Ciesielski, Saharon Shelah
Real Anal. Exchange 24(2): 615-620 (1998/1999).


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.


Download Citation

Krzysztof Ciesielski. Saharon Shelah. "Uniformly Antisymmetric Functions with Bounded Range." Real Anal. Exchange 24 (2) 615 - 620, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0968.26004
MathSciNet: MR1704738

Primary: 26A15

Keywords: Hamel basis , uniformly antisymmetric function

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
Back to Top