ABSTRACT

The reader who has been able to reach this place after having read the previous chapters might have realized that the proofs of a remarkable number of results follow a relatively small number of patterns. With this in mind, the purpose of this chapter is to collect several general techniques that generate or improve lineability. As a matter of fact, not many of such general criteria are known up to the moment. This is why this chapter is rather short. It should be said that many of the statements given in this book could have been demonstrated by using the mentioned criteria but, since it is mainly addressed to beginners, we have preferred to give more natural proofs for each statement and then, in a final chapter, to extract the deep essence of the proofs in a few results. There is, in addition, a historical reason for this. Namely, most lineability results appeared in an independent and isolated way; it was several years later when the (few) general techniques arose.