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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.


References [Enhancements On Off] (What's this?)

  • [1] L. E. J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann. 72 (1912), 37-54. MR 1511684
  • [2] M. H. A. Newman, Elements of the topology of plane sets of points, Cambridge Univ. Press, New York, 1961. MR 24 #A2374. MR 0132534 (24:A2374)
  • [3] S. A. Andrea, On homeomorphisms of the plane, and their embedding in flows, Bull. Amer. Math. Soc. 71 (1965), 381-383. MR 30 #2478. MR 0172258 (30:2478)
  • [4] -, On homeomorphisms of the plane which have no fixed points, Abh. Math. Sem. Univ. Hamburg 30 (1967), 61-74. MR 34 #8397. MR 0208588 (34:8397)

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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

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