1550251515-Classical_Complex_Analysis__Gonzalez_

Introduction

In this treatise we assume the reader to be familiar with the real number
system ~' as well as with the properties of the real functions of one or
several real variables, as developed in the usual courses in calculus and in
real variables. We assume also some acquaintance with the fundamental
concepts and propositions of abstract algebra and modern geometry.
In Chapter 2 we elaborate on some topological notions and properties
that are needed in complex analysis. In fact, many developments in topol-
ogy originated from certain questions in complex analysis and conversely,
a number of recent advances in analysis are topological in character, these
two branches of mathematics being closely related.
Since several instances of sets and mappings occur in Chapter 1, we
begin with a brief discussion of these notions.

0.1 Sets

The concepts of an element (or object) and a set (or class, collection, family,

system, aggregate) of elements are assumed to be intuitively clear. They

are regarded as primitive concepts, so we shall not attempt to define them. t

tFor an indirect definition in terms of axioms, see, for example, P. Suppes,

Axiomatic Set Theory, or J. E. Rubin, Set TheonJ for the Mathematician.

1