I've just finished a course on bilinear forms and am now starting a cause on topological spaces and was just wondering; for a metric space which is made up of a set $M$ and a metric function $d$ such that $d:M \times M \to \mathbb{R}$ defines the distance between points in $M$ etc etc..
Is this 'distance function' a simply a bilinear form? And if not why not? What goes wrong?
Thanks!