Fixed point sets of homeomorphisms of metric products

@inproceedings{Martin1988FixedPS,
  title={Fixed point sets of homeomorphisms of metric products},
  author={John R. Martin},
  year={1988}
}
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 S2n-1 as a factor, then A can be any nonempty closed subset. In the case where A is in Int(Bf2n+1), the interior of the closed unit (2n + 1)-ball B2n+l, a strong necessary condition is given. In particular… Expand
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References

SHOWING 1-9 OF 9 REFERENCES
On fixed point sets of homeomorphisms of then-ball
Conditions are investigated under which a subsetA can be the fixed point set of a homeomorphism ofBn. If eitherA ∩ ∂Bn ≠ Ø andn arbitrary orA ∩ ∂Bn=Ø andn even it is necessary and sufficient thatA isExpand
Fixed point sets of homeomorphisms of compact surfaces
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. AExpand
Lectures on Hilbert Cube Manifolds
Preliminaries Z-sets in Q Stability of Q-manifoldsitle> Z-sets in Q-manifolds Q-manifolds of the form $M \times [0, 1)$ Shapes of Z-sets in Q Near homeomorphisms and the Sum Theorem Applications ofExpand
Algebraic Topology: An Introduction
TLDR
Professor Massey's book developed from lecture notes of courses taught to Yale undergraduate and graduate students over a period of several years, and is the author of numerous research articles on algebraic topology and related topics. Expand
Fixed point sets of metric and nonmetric spaces
Introduction to Knot Theory
Knots and links, Math
  • J. Math
  • 1976
Lectures on Hubert cube manifolds, CBMS
  • Regional Conf. Ser. in Math.,
  • 1976
Fixed point sets.