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E13

[152]Prerequisites:categories of Baire Sec.Β [0MR].Difficulty:*.

Show that there is no function \(f:ℝ→ℝ\) which is continuous on the rational points and discontinuous on the irrational points. (Hint. Show that the set \(β„β§΅β„š\) of irrationals is not a \(F_𝜎\) set in \(ℝ\), using Baire’s theorem.)

Solution 1

[153]

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Authors: "Mennucci , Andrea C. G." .
Bibliography
Book index
  • Baire category
  • category, Baire
  • irrational numbers
  • function, discontinuous
  • F-sigma, \( ℝ \setminus β„š \)
  • continuous function
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