existence of a function that is continuous at every rational and discontinuous at every irrational

Question

Thomae's function gives the existance of a function continuous at every irrational number and discontinuous at every rational number. Is there existance of a function that is continuous at every rational and discontinuous at every irrational

score 1 · Answer 1 · answered Mar 08 '18 at 15:45

1

Wikipedia knows the answer to that. Read "Follow-up" at https://en.wikipedia.org/wiki/Thomae%27s_function

answered Mar 08 '18 at 15:45

Mario

932

existence of a function that is continuous at every rational and discontinuous at every irrational

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