Boundary

Summary

This chapter opened with a discussion about boundary points of subsets of a metric space. We then examined how boundary points relate to isolated points and accumulation points. We have talked about sets with empty boundary and how they relate to connectedness, and sets that include their boundaries (closed sets). We have explored boundaries of unions and intersections of sets. We have defined the Cantor set, more of which we shall see later. We have defined the closure and interior of subsets in terms of their boundaries. We have looked at the relationships that exist between closure and interior and have examined how they behave under the basic set-theoretic operations.