×

Uniformly antisymmetric functions with bounded range. (English) Zbl 0968.26004

Summary: The goal of this note is to construct a uniformly antisymmetric function \(f: \mathbb R \rightarrow \mathbb R\) with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson. A problem of existence of a uniformly antisymmetric function \(f:\mathbb R \rightarrow \mathbb R\) with finite range remains open.

MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A21 Classification of real functions; Baire classification of sets and functions
PDFBibTeX XMLCite
Full Text: arXiv