I found this definition but i don't know if it is correct or not ?
"A topological space X is normal if for every pair of closed disjoint sets A and B of X there exists $f: X\to [0; 1]$ continuous, such that $f(A) = \{0\}$ and $f (B) = \{1\}$"
I need a reference please if it is correct .
You may take this as the definition of "normal", but is unusual. The standard definition is this:
A topological space $X$ is normal if for every pair of disjoint closed sets $A$ and $B$ of $X$ there exist disjoint open subsets $U$ and $V$ of $X$ such $A \subset U$ and $B \subset V$ (in other words, if any two disjoint closed subsets $A$ and $B$ of $X$ have disjoint open neighborhoods).
Urysohn's lemma (see bof's comment) says that your definition is equivalent to the standard definition. It was proved by Pavel Samuilovich Urysohn in 1925.