[see also: collection, family]
Let $Q$ denote the set of positive definite forms on $V$ (including imprimitive ones, if there are any). [Not: “the set of the positive definite forms”]
We take $M$ to be the set of points in $V$ which map to a point $t$ in $A$.
Here the interesting questions are not about individual examples, but about the asymptotic behaviour of the set of examples as one or another of the invariants (such as the genus) goes to infinity.
[see also: put, establish, define]
Now $F$ is defined by setting $F(z)=$ ......
Setting $\alpha$ equal to $\beta$ in Corollary 3, we obtain ......
We claim that, by setting $w$ to zero on this interval, the value of $F(w)$ is reduced.
What sets the case $n=5$ apart is the fact that homotopic embeddings in a 5-manifold need not be isotopic.
By modifying the technique set out [= presented] in [3], we obtain ......
In Section 2 we set up notation and terminology. [= prepare]
On $TK$ we set up the symplectic structure induced by the metric. [= introduce]
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