"Let (f_n) be an increasing sequence of continuous functions on R. Suppose [tex]\forall x\in\mathbb{R}(f(x)=\lim_{n\rightarrow\infty}f_n(x))[/tex], and suppose that [tex]f(x)<\infty[/tex] for all x, prove that [tex]\{x\in\mathbb{R}:f(x)>a\}[/tex] is open for all a in R."(adsbygoogle = window.adsbygoogle || []).push({});

I think an additional condition of uniform convergence is required.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Open Set 2

**Physics Forums | Science Articles, Homework Help, Discussion**