This paper is closely connected to the work of M. Morley [Proc. Tarski Symp., Berkeley 1971, Proc. Symp. Pure Math. 25, 233-240 (1974; Zbl 0306.02051)]. Morley applies there topological type structures to model theory. Among other things, Morley gives abstract conditions for such topological structures to correspond to a theory in \(L_{\omega_ 1\omega}\). The present paper considers the following question. Assume that topological spaces \(Q_ 0,...,Q_ n\) satisfy Morley’s conditions. Under what assumptions it can be proved that an extension \((Q_ i)_{i<\omega}\) obtained by forming cartesian products also satisfies Morley’s conditions. E.g., in case \(n=2\) the compactness of \(Q_ j\), \(j\leq 2\), is needed.