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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the shift on the Cantor set


Author: Robbert Fokkink
Journal: Proc. Amer. Math. Soc. 112 (1991), 1153-1155
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1991-1069687-1
MathSciNet review: 1069687
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Abstract: Let $ O(x)$ be the orbit of $ x$ under a homeomorphism $ h$ on a metric space $ X$. It is shown that this motion can be found in the shift on the Cantor set; i.e. there is an embedding $ j = O(x) \to {\{ 0,1\} ^Z}$ such that $ \sigma \circ j = j \circ h$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1069687-1
Article copyright: © Copyright 1991 American Mathematical Society