Onat, Mehmet2025-03-232025-03-2320221017-060X1735-8515https://doi.org/10.1007/s41980-021-00581-zhttps://hdl.handle.net/11486/6730Clapp and Puppe (J. Reine Angew Math 418:1-29, 1991) proved that, if G is a torus or a p-torus, X is a path-connected G-space and Y is a finite-dimensional G-CW complex without fixed points, under certain cohomological conditions on X and Y, there is no equivariant map from X to Y. Also, Biasi and Mattos (Bull Braz Math Soc New Ser 37:127-137, 2006) proved that, again under certain cohomological conditions on X and Y, there is no equivariant map from X to Y provided that G is a compact Lie group and X, Y are path-connected, paracompact, free G-spaces. In this paper, our objective is to generalize these results for the actions of finite-dimensional pro-tori and compact groups, respectively.eninfo:eu-repo/semantics/closedAccessThe Borsuk-Ulam theoremThe equivariant cohomologyCompact groupsArticle4841339134910.1007/s41980-021-00581-z2-s2.0-85107174739Q2WOS:000658237500003Q2