Talk:Topology/Completeness

Q. Point out some property which are not topological. Q. Is mertrizability is a topological property ?

Metrizability is a topological property (see the various metrization theorems).

Also note that 'completeness' is a topological property in the sense that: A Tychonoff topological space is Cech-complete (it is a countable intersection of open sets in some (and thus every) Hausdorff compactification) if and only if there is a compatible uniformity which is complete.