ABSTRACT
There are many consequences when a function is continuous in intervals and other more extended domains. This chapter discusses the domains of continuous functions. Any boundary point must be a set of accumulation points. The chapter reviews the concept of intervals, which is provided as a subset of a set of specific forms such as infinite open interval form. Continuity at a set of points is possible but not guaranteed. The chapter discusses the intermediate value theorem for a set of intervals. Continuous images of intervals are provided as intervals. The chapter reviews continuous images of compact sets. Continuous functions on compact sets have an absolute minimum and an absolute maximum. The chapter explains continuity in terms of inverse images of open sets. Inverse images of open sets provided by continuous functions are open.
