[see also: though]
Although  deals mainly with the unit disc, most proofs are so constructed that they apply to more general situations.
Although these proofs run along similar lines, there are subtle adjustments necessary to fit the argument to each new situation.
Although the definition may seem artificial, it is actually very much in the spirit of Darbo's old argument in .
Now $f$ is independent of the choice of $\gamma$ (although the integral itself is not).
Thus, although we follow the general pattern of proof of Theorem A, we must also introduce new ideas to deal with the lack of product structure.
Although standard, the notion of a virtual vector bundle is not particularly well known.