Note: If A, B are sets, f: A → B, f is a bijection, we define f⁻¹: B → A, by f⁻¹(y) = x, such that y = f(x).
Now let A = [0, 2π) and B = unit circle, with usual metrics. Let's define f: A → B by f(ϴ) = (cosϴ, sinϴ). Then f is continuous and a bijection. Show that f⁻¹ is not continuous.
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