Let R be a commutative ring. We showed in an earlier paper that under the hypothesis that the complete ring of quotients of R was an injective R-module, then there was a full subcategory of the category of topological R-modules that was dual to a full subcategory of discrete R-modules. Here we show that there is even a full subcategory of the category of topological R-modules that is *-autonomous. The crucial tool in this is the the high wide subcategory of the chu category, described in the preceding talk.