Real Analysis Exchange

Uniformly Antisymmetric Functions with Bounded Range

Krzysztof Ciesielski and Saharon Shelah

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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

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}

Keywords
uniformly antisymmetric function Hamel basis

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


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