• Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)


A number of notions developed in the case of the real numbers will now be generalized to normed vector spaces systematically. Let S be a subset of a normed vector space. Let f : SF be a mapping of S into some normed vector space F, whose norm will also be denoted by ||. Let υ be adherent to S. We say that the limit of f(x) as x approaches υ exists, if there exists an element wF having the following property. Given ε, there exists δ such that for all xS satisfying
$$\left| {x - \upsilon } \right| < \delta $$
we have
$$\left| {f(x) - w} \right| < \varepsilon $$


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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