[see also: continue, generalize]
We can extend $f$ by zero to the whole $\Omega$.
Now $A$, $B$ and $C$ all extend to a small neighbourhood of $x$.
We extend $f$ to be homogeneous of degree 1.
We make $D$ a Poisson algebra by extending the Poisson bracket on $A$ by linearity.
We begin by extending Construction 2.1 to encompass $B$-algebras.
This procedure can be extended to take care of any number of terms.
This conclusion extends to the general diffraction problem.
Much of the foregoing can be extended to the noncompact case.
The method of proof of Theorem B can be adapted to extend the right-to-left direction of Mostowski's result by showing that ......
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