ABSTRACT
This chapter explores a related set property that is referred to as open. The definition of “open” will require that the set under inspection contains only points of a certain type – namely, interior points, which we define first along with the concept of boundary points. Because of the everyday use of the words “open” and “closed,” it is natural to anticipate that if something is not open, then it must be closed. This relationship does not hold when applying these terms to subsets of R. The intersection of finitely many open sets is open. The union of any collection of open sets is open.
