Every topological space is initial with respect to the canonical map e into a product of copies of the two point space {0,1} with {0} as the only nontrivial open set. It seems to us remarkable that certain classes of spaces can be neatly described in terms of their situation in the canonical product. Almost realcompact and almost compact T2 spaces where characterized as maximal T2 subspaces of the closure of e[X] in a canonical product in [1] and [3]. In trying to clarify the role of the maximal T2 condition, we were led to the notion of a y* situated subspace of a canonical product in terms of which we could characterize generalized almost compact spaces (not necessarily T2 ). We were also led to consider the dual notion of a y-situated space which provided the key to the description of compact topological spaces. It is this latter characterization that we now examine.