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We show that for any cohomogeneity one continuous action of a compactconnected Lie group $G$ on a closed topological manifold the equivariantcohomology equipped with its canonical $H^*(BG)$-module structure isCohen-Macaulay. The proof relies on the structure theorem for these actionsrecently obtained by Galaz-Garcia and Zarei. We generalize in this way ourprevious result concerning smooth actions.

Equivariant cohomology of cohomogeneity one actions: the topological case