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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 .doi:10.1090/s0002-9939-1991-1064906-x fatcat:ud2ft227wfhmhkv4i2uaurnzze