Mining top-k frequent closed itemsets was initially proposed and exactly solved by Wang et al. [IEEE Transactions on Knowledge and Data Engineering 17 (2005) 652-664]. However, in the literature, no research has ever considered the complexity of this problem. In this paper, we present a set of proofs showing that, in the general case, the problem of mining top-k frequent closed itemsets is not in APX. This indicates that heuristic algorithms rather than exact algorithms are preferred to solve the problem.