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 xt 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(ak)>1. [Note the inversion after only.]