Question 86
Let $G = \{f : [0, 1] \to [0, 1] \mid f \text{ is one to one and continuous}\}$, and $\circ$ be the function composition; $(G, \circ)$ is a group.
a) Give an example of an infinite subgroup $H$ of $G$, which contains nonincreasing functions and $H \neq G$.
b) Let $H$ be a finite subgroup of $G$. Prove that $H$ has at most 2 elements.
a) Give an example of an infinite subgroup $H$ of $G$, which contains nonincreasing functions and $H \neq G$.
b) Let $H$ be a finite subgroup of $G$. Prove that $H$ has at most 2 elements.