On representable linearly compact modules

For a flat $R-$module $F,$ we prove that $\operatorname{Hom}_{R}(F,-)$ is a functor from the category of linearly compact $R-$modules to itself and is exact. Moreover, $\operatorname{Hom}_{R}(F,M)$ is representable when $M$ is linearly compact and representable. This gives an affirmative answer to a question of L. Melkersson (1995) for linearly compact modules without the condition of finite Goldie dimension. The set of attached prime ideals of the co-localization $\operatorname{Hom}_{R}(R_{S},M)$ of a linearly compact representable $R-$module $M$ with respect to a multiplicative set $S$ in $R$ is described.