You are here

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 \(G\).


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.

To open this file please click here.

Average: 5 (1 vote)