  The Brouwer fixed-point theorem in topology states that for any continuous
mapping $f$ on a compact convex set into itself admits a fixed point, i.e., a
point $x_0$ such that $f(x_0)=x_0$. Under certain conditions, this fixed point
corresponds to the throat of a traversable wormhole, i.e., $b(r_0)=r_0$ for the
shape function $b=b(r)$. The possible existence of wormholes can therefore be
deduced from purely mathematical considerations without going beyond the
existing physical requirements.
