This paper extends the nonexistence result of Heifetz and Samet (Games Econ. Behav. 22 (1998) 260–273). They have shown that there exists no universal knowledge space to which every knowledge space can be mapped in a knowledge-preserving manner. We show that an analogous nonexistence result holds in the more general context of information structures. These structures can be viewed as generalizations of knowledge spaces that describe non-probabilistic beliefs.