# Math Help - Continuity and closure

1. ## Continuity and closure

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!!!

2. ## Re: Continuity and closure

Remember that if $f$ is a function defined on a metric space, then $f$ is continuous if and only if $\{f(x_n)\}$ converges to $f(x)$ whenever $\{x_n\}$ converges to $x$.