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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
    Commented Feb 26, 2015 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
    Commented Feb 26, 2015 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
    Commented Feb 26, 2015 at 14:16
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    $\begingroup$ @Gerald Edgar: I though the French tribu was a $\sigma$-algebra $\endgroup$
    – Henry
    Commented Feb 26, 2015 at 16:03

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The mob/clan terminology goes back to Alexander Wallace:

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