Analysis problem

1. Nov 11, 2008

AlexHall

I need to show if the following is true or false.

If the function f: (0,1)--> R is continuous in every irrational number x then f is continuous at every number.

Thank you
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 11, 2008

e(ho0n3

The answer is false: Define f by f(x) = 0 if x is irrational; and f(x) = 1/q where x = p/q, p coprime to q. This function is continuous at every irrational and discontinuous at all the rationals.

3. Nov 11, 2008