EDB — 139

Exercises

1. [139] Let \(f : ℝ → ℝ\) be defined as \(f (x) = 1\) if \(x ∈ ℝ ⧵ ℚ\), \(f(0)=0\), and \(f (x) = 1/q\) if \(|x| = p/q\) with \(p, q\) coprime integers, \(q\ge 1\). Show that f is continuous on \(ℝ ⧵ ℚ\) and discontinuous in every \(t ∈ ℚ\).

   Show that the described function is u.s.c.

   Solution 1

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