[see also: make]
We shall do this by showing that ......
This is done to simplify the notation.
As the space of Example 3 shows, complete regularity of $X$ is not enough to allow us to do that.
For binary strings, the algorithm does not do quite as well.
Recent improvements in the HL-method enable us to do better than this.
In fact, we can do even better, and prescribe finitely many derivatives at each point of $M$.
A geodesic which meets $bM$ does so either transversally or ......
We have not required $f$ to be compact, and we shall not do so except when explicitly stated.
This will hold for $n>1$ if it does for $n=1$.
Consequently, $A$ has all geodesics closed if and only if $B$ does.
We can do a heuristic calculation to see what the generator of $x_t$ must be.
In contrast to the previous example, membership of $D(A)$ does impose some restrictions on $f$.
We may (and do) assume that ......
The statement does appear in  but there is a simple gap in the sketch of proof supplied.
Only for $x=1$ does the limit exist.
In particular, for only finitely many $k$ do we have $F(a_k)>1$. [Note the inversion after only.]
In doing this we will also benefit from having the following notation.