**D. Kiguradze**

## On the Product of Separable Metric Spaces

**abstract:**

Some properties of the dimension function dim on the class
of separable metric spaces are studied by means of geometric construction
which can be realized in Euclidean spaces.
In particular, we prove that if $\dim (X\times Y)=\dim X+\dim Y$
for separable metric spaces $X$ and $Y$,
then there exists a pair of maps $f: X\to \bR^s$, $g: Y \to \bR^s$,
$s=\dim X+\dim Y$, with stable intersections.