Def 7.6

A function 𝑓:𝐼 is called sequentially continue if

(lim𝑛𝑥𝑛=𝑥)(lim𝑛𝑓(𝑥𝑛)=𝑓(𝑥))

Thm 8.1

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