Closure of bounded set is bounded? Topological space

Let $X$ be topological space, and $A \subseteq X$ that is bounded. Is the closure of $A$ also bounded?

This is true if $X$ is topological vector space, but is it if $X$ is only topological?

• What is your definition of closure? – Ilham Apr 23 '15 at 20:48
• And how to define boundedness without a metric – marwalix Apr 23 '15 at 20:48
• Is this a metric space? – Rellek Apr 23 '15 at 20:49
• Closure is well defined for a general topological space. – Sam Clearman Apr 23 '15 at 20:49
• @Yeah, I just wanted to know what he meant by closure in his course. So we could work with his definition to avoid wasting time when writing a proof. But as it stands boundedness is a metric property. – Ilham Apr 23 '15 at 20:50

If $X$ is only topological, "bounded" has no meaning.
If $X$ is a metric space, the answer is "yes", as the closure consists of points that are within $\epsilon$ of points in the set.