Editing Metrizable space (section)

==Properties==

Metrizable spaces inherit all topological properties from metric spaces. For example, they are [[Hausdorff space|Hausdorff]] [[paracompact]] spaces (and hence [[Normal space|normal]] and [[Tychonoff space|Tychonoff]]) and [[First-countable space|first-countable]].  However, some properties of the metric, such as [[Complete metric space|completeness]], cannot be said to be inherited. This is also true of other structures linked to the metric. A metrizable [[uniform space]], for example, may have a different set of [[Contraction mapping|contraction maps]] than a metric space to which it is homeomorphic.