View source for The set of all open balls of a metric space are able to generate a topology and are a basis for that topology

For a [[Metric space|metric space]] {{M|(X,d)}} there is a [[Topological space|topology]] which the metric induces on {{M|x}} that is the topology of all sets which are [[Open set|open in the metric sense]].

{{Todo|Proof that open sets in the metric space have the topological properties}}

{{Theorem|Topology}}