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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The set of second iterates is nowhere dense in $ C$


Author: Károly Simon
Journal: Proc. Amer. Math. Soc. 111 (1991), 1141-1150
MSC: Primary 58F08; Secondary 26A18, 54H20
MathSciNet review: 1033961
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Abstract: Let $ C$ denote the set of continuous functions mapping $ [0,1]$ into itself endowed with sup norm. It is proved that the set $ \{ f \circ f:f \in C\} $ is nowhere dense in $ C$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1033961-5
PII: S 0002-9939(1991)1033961-5
Article copyright: © Copyright 1991 American Mathematical Society