Solution
= Solution
A square model of the <torus> has one vertex, two edges and one face, so its <Euler characteristic> is zero. The connected-sum formula gives
$$
\boxed{\chi(\#^gT^2)=g\cdot0-2(g-1)=2-2g.}
$$
The real <projective plane> has a bigon model with one vertex, one edge and one face, hence characteristic one. Therefore
$$
\boxed{\chi(\#^h\mathbb{RP}^2)=h-2(h-1)=2-h.}
$$