1. Any metric space can be converted into a topological space such that an open ball in a metric space corresponds to a basis in the corresponding topology (metric spaces as a specialization of topological spaces ).(adsbygoogle = window.adsbygoogle || []).push({});

2. Any topological space can be converted into a metric space only if there is a metric d such that the topology induced by d corresponds to an original topology.

I am wondering if above statements are true or not.

As per #2, if #2 is right, what topological properties with which every #2 convertible (metrizable ?) topological space share?

Thanks in advance.

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# Metric space versus Topological space

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