  We set up a formalism, within the antenna subtraction framework, for
computing the production of a massive quark-antiquark pair in electron positron
collisions at next-to-next-to-leading order in the coupling $\alpha_s$ of
quantum chromodynamics at the differential level. Our formalism applies to the
calculation of any infrared-safe observable. We apply this set-up to the
production of top-quark top antiquark pairs in the continuum. We compute the
production cross section and several distributions. We determine, in
particular, the top-quark forward-backward asymmetry at order $\alpha_s^2$. Our
result agrees with previous computations of this observable.
