 For metric spaces (but not for general topological spaces) separability is equivalent to second-countability and also to the Lindelöf property.If formula_31 is a nonempty metric space and formula_125 then formula_126 is called a "pointed metric space", and formula_127 is called a "distinguished point".Note that a pointed metric space is just a nonempty metric space with attention drawn to its distinguished point, and that any nonempty metric space can be viewed as a pointed metric space.