# Math Help - Continuous functions in a metric space problem...

1. ## Continuous functions in a metric space problem...

With the following problem, would I do it by showing the the complement is open or by showing that it contains all it's limit points (or something else - if so, what)? I can't see in what way I would use either method.

Let (X,d) and (Y,e) be metric spaces, let f,g:X to Y be continuous. Prove that the set B = {x in X : f(x) = g(x)} is a closed subset of X.

2. I would show that the set contains all of its limit points.
If p is a limit point of the set then there is a sequence of points in B and $\left( {x_n } \right) \to p$.

Well what do you know about $f\left( {x_n } \right)$ and about $g\left( {x_n } \right)$?