Abstract
Every closed and non-empty subset of a compact surfaceS can be the fixed point set of a homeomorphism, andS also admits fixed point free homeomorphisms if it does not have the fixed point property. A partial extension to higher dimensions states that every closed and non-empty subset of a compactn-manifold can be the fixed point set of a surjective self-map.
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References
R. F. Brown,Path fields on manifolds, Trans. Amer. Math. Soc.118 (1965), 180–191.
R. F. Brown and E. Fadell,Nonsingular path fields on compact topological manifolds, Proc. Amer. Math. Soc.16 (1965), 1342–1349.
H. Schirmer,On fixed point sets of homeomorphisms of the n-ball, Israel J. Math.7 (1969), 46–50.
H. Schirmer,Properties of fixed point sets on dendrites,36 (1971), Pacific J. Math. 795–810.
H. Schirmer,Fixed point sets of homeomorphisms on dendrites, to appear in Fund. Math.
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This research was partially supported by the National Research Council of Canada (Grant A 7579).
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Schirmer, H. Fixed point sets of homeomorphisms of compact surfaces. Israel J. Math. 10, 373–378 (1971). https://doi.org/10.1007/BF02771655
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DOI: https://doi.org/10.1007/BF02771655