Sequences in Normed Spaces
Alberto Guzmán · Birkhäuser Boston eBooks · 2002
Our mission is to study continuous functions. To discuss continuity, we must introduce the concept of limit. Our tools will be sequences, whose convergence we define in terms of distance tending to zero. Since we defined (Section 1.5) distance in terms of length in R n —and more generally, in terms of a norm in a vector space—we will cast our material in the language of norms.