Is a Function Continuous If It Maps Closure to Closure in Metric Spaces?

[Majrou]

Hi,
can anyone help me ?

Given Topological Spaces (metric spaces) (X, d1) and (Y,d2), show that a function f: X -> Y is continuous if and only if f(cl of A) is a subset of cl of f(A) for all A subset X1.

How can i proof this ?

Thank you!

 

[micromass]

What is your definition of continuous?? What properties did you see already about continuity??

What did you try already to solve this problem??