The plane is not compactly generated by a free mapping
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- by S. A. Andrea PDF
- Trans. Amer. Math. Soc. 151 (1970), 481-498 Request permission
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
- L. E. J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann. 72 (1912), no. 1, 37–54 (German). MR 1511684, DOI 10.1007/BF01456888
- M. H. A. Newman, Elements of the topology of plane sets of points, Cambridge University Press, New York, 1961. Second edition, reprinted. MR 0132534
- S. A. Andrea, On homeomorphisms of the plane, and their embedding in flows, Bull. Amer. Math. Soc. 71 (1965), 381–383. MR 172258, DOI 10.1090/S0002-9904-1965-11304-0
- Stephen A. Andrea, On homoeomorphisms of the plane which have no fixed points, Abh. Math. Sem. Univ. Hamburg 30 (1967), 61–74. MR 208588, DOI 10.1007/BF02993992
Additional Information
- © Copyright 1970 American Mathematical Society
- 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