Let $f$ be a real valued function on $\mathbb R.$ Consider the functions $$w_j(x)=\sup\{|f(u)-f(v)|:u,v\in[x-\frac{1}{j},x+\frac{1}{j}]\},$$ where $j\in \mathbb Z^+$ and $x\in\mathbb R.$ Define next,
$$A_{j,n}=\{x\in\mathbb R:w_j(x)<\frac{1}{n}\},n=1,2,\cdots$$ and $$A_n=\cup_{j=1}^{\infty}A_{j,n},n=1,2,\cdots$$ Now let $C=\{x\in\mathbb R:f$ is continuous at $x\}.$ How can we express $C$ in terms of the sets $A_n$?
