Can continuity of inverse be omitted from the definition of topological group? According to Wikipedia, a topological group $G$ is a group and a topological space such that 
$$ (x,y) \mapsto xy$$ and
$$ x \mapsto x^{-1}$$
are continuous. The second requirement follows from the first one, no? (by taking $y=0, x=-x$ in the first requirement)
So we can drop it in the definition, right?

There is even a term for a group endowed with a topology such that multiplication is continuous (but inversion need not be): a paratopological group.
