The book I'm reading doesn't explicitly give a definition of separable metric spaces. The only type of separability definition I know that a separable topological space is one that has a countable dense subset.
Could someone give me a definition of a separable metric space? I'm assuming it would have something to do with the metric that induces the topology, but I'm unsure as to how to write this.
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$\begingroup$Any metric space is a topological space. So topological terms generally have the same meaning as in a general topological space.
In particular a metric space is separable if it has a countable dense set.
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