Clapp 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.

Clapp 和 Puppe (J. Reine Angew Math 418:1–29, 1991) 证明，如果G是环面或p环面，则X是路径连接的G空间，Y是有限维G - CW没有不动点的复数，在X和Y上一定的上同调条件下，从X到Y不存在等变映射。此外，Biasi 和 Mattos（Bull Braz Math Soc New Ser 37:127–137, 2006）证明，同样在X和Y 的某些上同调条件下，没有从X到Y 的等变映射，前提是G是紧李群，X , Y是路径连通的、超紧的、自由G空间。在本文中，我们的目标是将这些结果分别推广到有限维 pro-tori 和紧致群的动作。