D. Kiguradze

On the Product of Separable Metric Spaces

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.