Topological product of \(o\)-compact and \(o\)-Lindelöf spaces (Q1405913)

The authors discuss \(o\)-compactness and \(o\)-Lindelöfness (for definitions see [\textit{R. Engelking}, ``General topology'', Heldermann Verlag, Berlin (1989; Zbl 0684.54001)] from the point of view of being preserved by the multiplication operation. Examples are cited which show that \(o\)-compactness and \(o\)-Lindelöfness are not finally multiplicative. It is proved that in the class of locally Čech complete spaces these properties are preserved by countable products.