sequentially continue

Def 7.6

A function $f:I⟶\mathbb{R}$ is called sequentially continue if

$$(\underset{n}{\lim }{x}_n=x)⟹(\underset{n}{\lim }f(x_n)=f(x))$$

Thm 8.1

All sequentially continue function on $[a,b]$ attain it’s maximum