# A Characterization of the Set of Points of Continuity of a Real Function

by Sung Soo Kim

American Mathematical Monthly
March, 1999

Subject classification(s): Analysis | Real Analysis | Continuity | Metric Spaces | Geometry and Topology | Topology | Point Set Topology
Applicable Course(s): 4.11 Advanced Calc I, II, & Real Analysis | 4.20 Topology

Let $$X$$ be a nonempty metric space without isolated points.  If $$G$$ is a countable intersection of open sets, the author shows that there is a function $$\phi (x)$$ that is continuous exactly on $$G$$.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.