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A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.

Who used these words with these meanings first and when? Why were these words chosen? I'm guessing it's a play on "group", but is it really?

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  • $\begingroup$ There are connotations of organisation: a "clan" is more highly structured than a "mob" both in everyday English and in mathematics. $\endgroup$ – James Cranch Feb 26 '15 at 12:12
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    $\begingroup$ I normally associate these terms with Wallace who was the father of topological semigroup theory. But these names are a bit silly and I don't think anybody uses them anymore. In the introduction of the book Elements of Compact Semigroups Hoffman and Mostert state they are going to call things by intuitive names like compact semigroup with identity instead of clan, etc $\endgroup$ – Benjamin Steinberg Feb 26 '15 at 12:49
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    $\begingroup$ "Group", "family", "collection" have already been used. Bourbaki used tribu ("tribe"), but that did not catch on outside French-speakers. So Alexander just used some other words for organization. $\endgroup$ – Gerald Edgar Feb 26 '15 at 14:16
  • $\begingroup$ @Gerald Edgar: I though the French tribu was a $\sigma$-algebra $\endgroup$ – Henry Feb 26 '15 at 16:03
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The mob/clan terminology goes back to Alexander Wallace:

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