[see also: stroke]
Its role is to rule out having two or more consecutive $P$-moves (on the grounds that they can be performed in one go).
a path obtained by going from $A$ to $B$ along the lower half of the circle
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.
This proves that the dimension of $S$ does not go below $q$.
We adopt the convention that the first coordinate $i$ increases as one goes downwards, and the second coordinate $j$ increases as one goes from left to right.
Some members go into more than one $V_k$.
To go into this in detail would take us too far afield.
We now go through the clauses of Definition 3.
Before going to the proof, it is worth noting that ......
This idea goes back at least as far as .
This argument goes back to Banach.
Many of these results are known, and indeed they go back to the seminal paper of Dixmier [D] of 1951.
Going back to the existential step of the proof, suppose that ......
Before we go on, we need a few facts about the spaces $L_p$.
The equation $PK=0$ then goes over to $QK=0$.
The rest of the proof goes through as for Corollary 2, with hardly any changes.
There are kneading sequences for which the arguments of Section 4 go through routinely.