Fixed point sets of homeomorphisms of metric products
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- by John R. Martin PDF
- Proc. Amer. Math. Soc. 103 (1988), 1293-1298 Request permission
Abstract:
In this paper it is investigated as to when a nonempty closed subset $A$ of a metric product $X$ containing intervals or spheres as factors can be the fixed point set of an autohomeomorphism of $X$. It is shown that if $X$ is the Hilbert cube $Q$ or contains either the real line $R$ or a $(2n - 1)$-sphere ${S^{2n - 1}}$ as a factor, then $A$ can be any nonempty closed subset. In the case where $A$ is in $\operatorname {Int}({B^{2n + 1}}{\text {)}}$, the interior of the closed unit $(2n + 1) - {\text {ball }}{B^{2n + 1}},$, a strong necessary condition is given. In particular, for ${B^3},A$ can neither be a nonamphicheiral knot nor a standard closed or nonplanar bordered surface.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1293-1298
- MSC: Primary 55M20; Secondary 54H25, 57M25, 57N99
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955025-9
- MathSciNet review: 955025