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

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
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: http://dx.doi.org/10.1090/S0002-9939-1975-0367953-7
PII: S 0002-9939(1975)0367953-7
Keywords: Topological entropy, nonwandering set
Article copyright: © Copyright 1975 American Mathematical Society