Let $f : [a, b] \longrightarrow \mathbf{R}$ be a continuous function. Prove that the restriction $g$ of the function $f$ to the interval $]a, b[$ belongs to the set $\mathscr{D}_{a,b}$.
Let $f : [a, b] \longrightarrow \mathbf{R}$ be a continuous function. Prove that the restriction $g$ of the function $f$ to the interval $]a, b[$ belongs to the set $\mathscr{D}_{a,b}$.