Translator Disclaimer
2022 A Characterization of Attractors for Baire Functions on the Interval
E. S. Coulam, T.H. Steele
Author Affiliations +
Real Anal. Exchange 47(1): 135-146 (2022). DOI: 10.14321/realanalexch.47.1.1613920060

Abstract

We show that for any closed set $E\subset \lbrack 0,1]$, there exists $f:[0,1]\rightarrow \lbrack 0,1]$ in the first class of Baire that generates $E$ as one of its $\omega $-limit sets. Since $\omega $-limit sets are necessarily closed, this characterizes the class of $\omega $-limit sets for Baire or Borel functions on the interval.

Citation

Download Citation

E. S. Coulam. T.H. Steele. "A Characterization of Attractors for Baire Functions on the Interval." Real Anal. Exchange 47 (1) 135 - 146, 2022. https://doi.org/10.14321/realanalexch.47.1.1613920060

Information

Published: 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.14321/realanalexch.47.1.1613920060

Subjects:
Primary: 26A18 , 54H25
Secondary: 37B99

Keywords: $\omega $-limit set , Baire function , Borel function

Rights: Copyright © 2022 Michigan State University Press

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • 2022
Back to Top