General topology

Abstract

In this chapter we briefly review the basic facts about general topology that will be used in this book. We omit many of the most basic definitions, and some of the proofs. (The topic of convergence of nets, by contrast, is treated in full detail.) For definitions of terms used below without definition, and for proofs of theorems stated without proof, the reader is referred to any textbook on general topology, e.g., [40], [11], or [20]. To begin with, the terms topology, topological space, open set, closed set, interior, closure, boundary, and neighborhood, will be used without explanation, and the various relations between these notions will be assumed known. The interior of a set A in a topological space will be denoted by A°, the closure of A by A⁻, and the boundary of A by ∂A.