Fixed points of orientation reversing homeomorphisms of the plane

Kuperberg, Krystyna

doi:10.1090/S0002-9939-1991-1064906-X

Fixed points of orientation reversing homeomorphisms of the plane
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by Krystyna Kuperberg PDF

Proc. Amer. Math. Soc. 112 (1991), 223-229 Request permission

Abstract:

Let $h$ be an orientation reversing homeomorphism of the plane onto itself. If $X$ is a plane continuum invariant under $h$, then $h$ has a fixed point in $X$. Furthermore, if at least one of the bounded complementary domains of $X$ is invariant under $h$, then $h$ has at least two fixed points in $X$.

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