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The Borel structure of iterates of continuous functions

Published online by Cambridge University Press:  20 January 2009

Paul D. Humke  and
M. Laczkovich
Paul D. Humke
Affiliation:
Department of MathematicsSt. Olaf CollegeNorthfield, MN, U.S.A.
M. Laczkovich
Affiliation:
Department of AnalysisEötvös Lorand UniversityBudapest, Hungary
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Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.

We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 483 - 494
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCE

1.Kuratowski, K., Topology I (Academic Press, 1966).Google Scholar