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We obtain under a less restrictive hypothesis a Borsuk-Ulam type result of Munkholm’s in which the antipodal map is replaced by a      Z p {Z_p}      -action on a cohomology  n -sphere.

A stronger Borsuk-Ulam type theorem for proper 𝑍_{𝑝}-actions on 𝑚𝑜𝑑𝑝 homology 𝑛-spheres