## Real Analysis Exchange

### Towards a characterization of ω-limit sets for Lipschitz functions

T. H. Steele

#### Abstract

Recent research has shown that there is a significant cleavage between the structure of ω sets for continuous functions, and the structure of ω-limit sets for Lipschitz functions. While every non-empty nowhere dense compact set is an ω-limit set for a continuous function, most of these sets cannot be an attractor for a Lipschitz function. When one considers the topological structure of these two classes of ω-limit sets, however, there is no such divergence. In this paper we investigate the necessarily measure based structural differences between these two classes of sets. We then use these results to work towards a characterization of ω-limit sets for Lipschitz functions.

#### Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 201-212.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515215

Mathematical Reviews number (MathSciNet)
MR1433608

Keywords
ω limit set Lipschitz function

#### Citation

Steele, T. H. Towards a characterization of ω-limit sets for Lipschitz functions. Real Anal. Exchange 22 (1996), no. 1, 201--212. https://projecteuclid.org/euclid.rae/1338515215

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