Decide whether the following properties of metric spaces are topological or not I have to decide whether the following properties of metric spaces are 'topological' or not,
(a) every continuous function on M is bounded
(b) $(\forall x \in M)(\forall y \in M) d(x; y) > 0$
(c) $(\forall x \in M)(\forall y \in M) d(x; y) > 1$
Where M is a metric space with metric d. 
but looking through my notes.. i can't find any distinct definition of what 'topological' means. Would anyone be able to clear this up?

In short, a property of a metric space is topological if it does not (really) depend on the metric. That is, if you have a different metric that produces the same notions of convergence, continuous functions, etc. (or even if you only have the notions of convergence, contnuou functions, etc.) then the property does not change.
Note that $b$ and $c$ can be greatly simplified to a truth value that holds completely independently of the metric $d$; which makes at least these properies topological. 
