Subnormal spaces and a Dowker-type problem

In the present paper the class of subnormal spaces — the spaces in which any two closed disjoint sets can be separated by disjoint $G_\delta$ sets — is considered. It is proved that the product of a space $X$ by the closed real interval (or by any $\sigma$-compact Hausdorff space with countable network) is subnormal provided that $X$ is subnormal and countably metacompact. An example of a weakly normal space which is not subnormal is presented.