Real Analysis Exchange
- Real Anal. Exchange
- Volume 26, Number 1 (2000), 201-216.
The Essential Point Set of a Continuous Function
For continuous self maps of $[0,1]$, we extend M. K. Fort, Jr.'s notion of an essential fixed point to points generating nonsingleton $\omega $-limit sets. The $\omega $-limit sets of these essential points are, in a metric sense, stable under small perturbations of the function. We develop some of the properties of the essential point set of a continuous function, and investigate the relationship between essential points, $\omega $-limit sets, and the chaotic nature of the generating function.
Real Anal. Exchange, Volume 26, Number 1 (2000), 201-216.
First available in Project Euclid: 2 January 2009
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Steele, T. H. The Essential Point Set of a Continuous Function. Real Anal. Exchange 26 (2000), no. 1, 201--216. https://projecteuclid.org/euclid.rae/1230939154