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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The plane is not compactly generated by a free mapping


Author: S. A. Andrea
Journal: Trans. Amer. Math. Soc. 151 (1970), 481-498
MSC: Primary 54.75
DOI: https://doi.org/10.1090/S0002-9947-1970-0267543-0
MathSciNet review: 0267543
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Abstract: Let X denote the plane, or the closed half-plane, and let $ T:X \to X$ be a self homeomorphism which preserves orientation and has no fixed points. It is proved that, if A is any compact subset of X, then there exists an unbounded connected subset B of X which does not meet $ {T^n}(A)$ for any integer n.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0267543-0
Keywords: Free mapping, flow line, edge point, edge point type, ray, side domain, regular domain
Article copyright: © Copyright 1970 American Mathematical Society