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I was wondering about this topic. Is there a connection between the $T_n$ separation axioms and separability itself?

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    It's probably clear why the $T_n$-axioms are called separation axioms (T stands for German *Trennung* -- "separation"; these axioms go back to the topology book of Alexandroff-Hopf; see [here](http://projecteuclid.org/euclid.bams/1183499379) for a review). The term *separability* goes back to Fréchet, see [here](http://mathoverflow.net/questions/51494) and [here](http://math.stackexchange.com/q/63793/5363) for some historical background.2012-08-13

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No; there is no real connection between the two notions. There are both separable and non-separable spaces with any of the separation axioms.

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    @Qiaochu: While there may be a diachronic connection, synchronically there is none. However, I’ve rephrased it.2012-08-12