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**wopashui** Let (M,d),(N,p),(Y,q) be metric spaces. A function f:MxN-->Y is called separately continuous if for every $\displaystyle a\in M $ and $\displaystyle b \in M$, the function $\displaystyle g:N-->Y$ and $\displaystyle h:M-->Y$, given by $\displaystyle g(y)=f(a,y)$ and $\displaystyle h(x)=f(x,b)$, are continuous.

Prove that every continuous function f:MxN-->Y is separately continuous.

the deinition given is confusing, I have not done any separately continuous question before, need some help here.