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Abstract
Recently, J. Smítal and T.H. Steele [J. Difference Equ. Appl. 15 (2009), 77–86] considered the mappings C and NW, which take a function to its centre
, and to its set of non-wandering points
, respectively. They characterize a function
at which maps C and NW are continuous, and put a problem whether the same characterization is true for the map CR, which takes an
to its set of chain recurrent points
. We show that the answer is positive.
Keywords:
Acknowledgements
The research was supported, in part, by project MSM 4781305904 from the Czech Ministry of Education. The author would like to thank her supervisor Professor Marta Štefánková for fruitful discussions, Professor James A. Yorke for taking her attention to [Citation4], and the referees for valuable comments.