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**Homework Statement**

Let C be the set of points where f: R --> R is continuous. Show that C may be written as the intersection of a countable collection of open sets in R.

**The attempt at a solution**

If C is empty, the result is true. If C has countably many points, say x_0, x_1, ..., then R - {x_0, x_1, ...} is the union of countable collection of open intervals, (a_i, b_i) and so we may write C as the intersection of {[a_i, b_i]}. Of course, this is not what I want, but it's the best idea I've had so far. I don't know what to do if C is uncountable. Any tips?