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G-spaces and Fixed Point Sets

Research paper by Karl Heinrich Hofmann, John R. Martin

Indexed on: 01 Dec '00Published on: 01 Dec '00Published in: Geometriae Dedicata



Abstract

For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact group with nonsingleton components, every closed subset is the fixed point set of an autohomeomorphism if and only if the weight of the whole group is not bigger than that of the component of the identity.