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A problem on topological transformations of the plane. II

Published online by Cambridge University Press:  24 October 2008

A. S. Besicovitch
A. S. Besicovitch
Affiliation:
Trinity CollegeCambridge
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Extract

In the paper under the above title I have given an example of a homoeomorphism of a plane under which the positive half-orbit† of a certain point is everywhere dense on the plane, and I have made a statement that the same is true for every point of the plane, except the origin.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 38 - 45
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

* Fundamenta Math. 28 (1937), 61–5.Google Scholar

† Given a homoeomorphism y = Tx, the set of points T nx for all integral n is the orbit of x. Half the set corresponding to positive (negative) values of n is the positive (negative) half-orbit.