[NBHM_2006_PhD Screening Test_Analysis]
Let $f$ be a real valued function on $\mathbb{R}$ define $w_j(x)=\sup\{|f(u)-f(v)|: u,v\in [x-1/j,x+1/j]\}$ $j\in \mathbb{N}$ and $x\in\mathbb{R}$, Define next $A_{j,n}=\{x\in\mathbb{R}:w_j(x)<1/n\}$ $n=1,2,\dots$ and $A_n=\bigcup_{j=1}^{\infty}A_{j,n}$ Now let $C=\{x\in\mathbb{R}: f > \text{ is continuos at }x\}$ How to express $C$ interms of $A_n$?
Well, according to the definition, $f$ iss continuos at $x$ iff $w_j(x)=0$ (I guess, I can do that by definition of continuity).
Then I guess, $C=\bigcap A_n$. I am not sure. Thank you.