Re: Continuity of function

Steve wrote:

In terms of continuity what is the status of a function defined such as f(x)=0 for x element of Q and f(x)=1 otherwise. It seems as if it is nowhere continuous. Its been a long time since I've looked at analysis so is it a theorem that if f continuous a a point x then it is continuous for every point in some neighborhood about x. Is there a name for this theorem?



Your function f is continuous nowhere. The "theorem" is false: Consider g(x) = 0 if x is rational, x if x is irrational. Then g is continuous at 0 only.

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Stephen J. Herschkorn                        sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

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