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

by Sung Soo Kim

This article originally appeared in:
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 \(G\).

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