Analogous results to two classical characterizations of covering properties by products

First, as an analogue of Dowkerʹs theorem for countable paracompactness, we prove a characterization of countable metacompactness in terms of subnormality of products. Second, as an analogue of Tamanoʹs theorem for paracompactness, we give a characterization of Lindelِfness in terms of normality of products.