On colimits of classifying spaces. This topologist may be missing something, but the conclusion seems obviously true, at least in reasonable situations. With a countable system of inclusions of spaces, unless the situation is fairly bizarre, the system will be filtered and we can find a countable cofinal sequence. But finite products commute with sequential colimits in reasonable categories of spaces. Since the usual classifying space of G is constructed as the geometric realization of a simplicial space whose space of q-simplices is G^q, and since geometric realization certainly commutes with sequential colimits, the conclusion seems clear. It is used all the time in algebraic topology, in such familiar examples as BU = colim BU(n), BTop = colim BTop(n), BF = colim BF(n), etc, the last being a system of monoids rather than groups. In the standard classical statement that BU classifies stable complex vector bundles, we are using the first listed special case. While the groups are compact in that case, compactness is not relevant to the argument and fails for the groups Top(n), for example. In more complicated equivariant situations, one has countable systems that are not naturally sequential, but again the conclusion is familiar and in common use. Peter