Isomorphisme of measurable space 
Hi, 
Can you ,help me to understand this proposition, and it's prrof ?

Definition 24 is :
A measurable space $(T, \mathcal{T})$ is said to be separable if there
  existe a sequence $(A_n)$ dans $\mathcal{T}$ which generates
  $\mathcal{T}$ and $\chi_{A_n}$ separate the points of $T$

Please 
Thank you 

Clearly, $h:T\to h(T)$ is a surjection. The fact that $h$ is an injection follows from the fact that $\{1_{A_n}\}_{n\in \Bbb N}$ separate points of $T$. That is, if $t\neq s$ then $h(t)\neq h(s)$ since for some $n$ it holds that there exists a separation indicator function, that is $1_{A_n}(t)\neq 1_{A_n}(s)$.
I didn't get your second confusion, could you elaborate?
