In the present chapter, we are concerned with sequence spaces over a complete, non-trivially valued field K, Archimedean or non-Archimedean. It will be stated explicitly in the relevant context when the field is Archimedean or non-Archimedean. More particularly, we study the family c 0(p) of sequence spaces defined in Chapter 1 (see Definition 20). Unlike the earlier chapters, we write the sequence {x k }, beginning with k = 1, for the sake of convenience.