Abstract
In this paper we shall deal with a weak version of the Borsuk-Ulam theorem for G-isovariant maps, which we call the weak isovariant Borsuk-Ulam theorem. One of the results is that the weak isovariant Borsuk-Ulam theorem in linear G-spheres holds for an arbitrary compact Lie group G. On the contrary the weak isovariant Borsuk-Ulam theorem in semilinear G-(homology) spheres holds if and only if G is solvable.
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