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Noncontinuity of topological entropy of maps of the Cantor set and of the interval


Author: Louis Block
Journal: Proc. Amer. Math. Soc. 50 (1975), 388-393
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1975-0367953-7
MathSciNet review: 0367953
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Abstract: We show that topological entropy, as a map on the space of continuous functions of the Cantor set into itself, is not continuous anywhere. Furthermore, topological entropy, as a map on the space of continuous functions of the interval into itself, is not continuous at any map with finite entropy.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367953-7
Keywords: Topological entropy, nonwandering set
Article copyright: © Copyright 1975 American Mathematical Society

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