Open Sets and Continuity

Abstract

In this chapter we shift our attention from functions back to sets. The shift is prompted by the fact that continuous functions have a natural description in terms of sets: the so-called open sets. Just as continuous functions may be viewed as the simplest functions, open sets may be viewed as the simplest sets. And just as complicated functions arise from continuous functions by the limit process, complicated sets arise from open sets by certain operations, namely, complementation and countable union.