Q:

queston about T4- spaces

please can can anyone tell me that is it is true?
i found this statement (question) in one old book of topology. i think it is just printing mistake.
statement(question) is 
prove that every T4 space is T0 space. 
  i had tried to prove but fail. i know that in T4 space every two
disjoint closed sets have disjoint open
neighborhoods but how to prove it T0,  is the question is wrong. please help me

A:

The separation axioms are defined in such a way, that there are increasingly stronger:
$$
T_4 \Longrightarrow T_3 \Longrightarrow  T_2 \Longrightarrow  T_1 \Longrightarrow T_0.
$$
There is sometimes some confusion about the "names" of spaces satisfying certain separation axioms. For example, "normal" does not imply $T_0$ and "regular" does not imply $T_0$, see here. Hence "normal" does not imply $T_4$.

