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Fixed points of the bucket handle

Author(s): Jan M. Aarts; Robbert J. Fokkink
Journal: Proc. Amer. Math. Soc. 126 (1998), 881-885.
MSC (1991): Primary 54H25, 54F15; Secondary 54H11
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Abstract: If a homeomorphism on the bucket handle has an invariant composant, it has a fixed point in that composant. It follows that a homeomorphism on the bucket handle has at least two fixed points. Our methods apply to general Knaster continua.

References:

1.: J. M. Aarts and R. J. Fokkink, On composants of the bucket handle, Fundamenta Mathematicae 139 (1991), 194-208. MR 93a:54030
2.: A. Beck, Continuous flows in the plane, Springer, Berlin 1974. MR 58:18379
3.: H. Cook, W. T. Ingram and A. Lelek, A list of problems known as Houston Problem Book, Continua with the Houston problem book, H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek and P. Minc (eds), Lecture Notes in pure and applied mathematics 170, Marcel Dekker, New York (N.Y.) 1995, 365-398. MR 96f:54042
4.: D. van Dantzig, Ueber topologisch homogene Kontinua, Fundamenta Mathematicae 14 (1930), 102-125.


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