The space C(X) of all continuous functions on a compact space X
carries the structure of a normed vector space, an algebra and a
lattice. On the one hand we study the relations between these
structures and the topology of X, on the other hand we discuss a
number of classical results according to which an algebra or a
vector lattice can be represented as a C(X). Various applications
of these theorems are given.Some attention is devoted to related
theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz
Representation Theorem.The book is functional analytic in
character. It does not presuppose much knowledge of functional
analysis; it contains introductions into subjects such as the weak
topology, vector lattices and (some) integration theory.
General
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