Map $f:I\to I$ is a continuous map of the interval $I$ to itself. $J$ is a compact subinterval of $I$, say

$J=[a,b] \subseteq I$ with $a < b$.
Dr. Abdulla

Regarding Lemma 4, the $J$’s are compact subintervals, what are they a subinterval of? I am just trying to understand that part while watching this lecture, I know it has nothing to do with the proof, but for my knowledge I was curious.

Thanks

]]>For an overview of LaTeX mathematics notation, look to one of the following references: 1, 2, and any others you find online.

For example,

\[ u_t-(u^m)_{xx} +b u^\beta=0\]

produces

\[ u_t-(u^m)_{xx} +b u^\beta=0\]