On the topological completion of $M$-space products

Abstract:

Using the continuum hypothesis, an example is given of two countably compact spaces X and Y such that $X \times Y$ is an M-space, but is not countably compact. If $\mu X$ denotes the completion of X with respect to its finest uniformity, the above example shows that $\mu (X \times Y)$ is not necessarily equal to $\mu X \times \mu Y$, even though $X \times Y$ is an M-space.