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Motivation for the term “separable” in topology

A topological space with a countable dense subset is called separable. I was wondering if there is some particular reason to use the word "separable", given that separable space is sometimes easy to be confused as one of the separation axioms, but actually they do not have similar meanings at least to me? Does it capture some intuition of this concept? Thanks and regards!

  • $\begingroup$ Shall I delete mine? After a quick glance at the reply there, it seems to suggest the name comes from the special case of $\mathbb{Q}$ dense in $\mathbb{R}$. But how about in general topological spaces? $\endgroup$ – StackExchange for All Feb 4 '12 at 6:31
  • $\begingroup$ Things frequently get their names from suggestive special cases. You shouldn't expect the idea behind the name to apply to all cases. $\endgroup$ – Qiaochu Yuan Feb 4 '12 at 6:34
  • $\begingroup$ Sometimes at the risk of being confused with other concepts. I doubt if it is worth it. $\endgroup$ – StackExchange for All Feb 4 '12 at 6:35

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